Money and Financial Markets (Module MW21.1) - uni-jena.de · PD Dr. M. Pasche Friedrich Schiller...

Money and Financial Markets

(Module MW21.1)

PD Dr. M. Pasche

Friedrich Schiller University Jena

Work in progress! Bug Report to: [email protected]

S.1

Outline:

1. Financial Markets

1.1 Overview over Financial Markets1.2 Interest Rate Theory

2. Theory of Financial Structure

2.1 Financial Intermediates2.2 Management of Return, Risk and Liquidity2.3 Adverse Selection Problems2.4 Moral Hazard Problems2.5 Efficient Market Hypothesis and its Limits

3. The Money Supply Process

3.1 Function and Measurement of Money3.2 Creation of Central Bank Money3.3 Deposit Creation and the Multiplier3.4 Endogenous Money Supply

S.2

4. Theory of Money Demand

4.1 Keynesian Theory of Liquidity Preference4.2 Portfolio Theory of Money Demand4.3 Money Demand in Intetemporal Choice of Households

5. Central Banking and Transmission of Policy

5.1 Goals of Monetary Policy5.2 Transmission Channels5.3 Targets, Strategies, and Rules5.4 The Taylor Rule5.5 Unconventional Measures

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Basic Literature:

I Mishkin, Frederic S. (2012), The Economics of Money,Banking, and Financial Markets, 10th ed., Boston et al:Pearson International Edition.

I Bailey, Roy E. (2005), The Economics of Financial Markets,Cambridge: Cambridge University Press.

I Bofinger, Peter (2001), Monetary Policy: Goals, Institutions,Strategies, and Instruments. Oxford: Oxford University Press.

References to more specific literature can be found in the slidecollection.

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Preliminary schedule (summer 2018):

Week Tuesday Friday

15 ch.1 –16 ch.1 –17 ch.2 ch.2

18 –∗) exercise19 ch.2 exercise20 ch.2 exercise21 ch.2 exercise22 midterm23 ch.3 ch. 324 ch.3 –25 ch.4 exercise26 ch.4 exercise27 ch.5 exercise28 ch.5 exercise

∗) public holiday

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Type of course:

I Basic elective

I 4 hours per week, 6 ECTS

Examination:

I 60 min. midterm exam (40%)

I 60 min. endterm exam (60%)

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1. Financial Markets1.1 Overview over Financial Markets

Outline:

1.1.1 Asset Market Classifications

1.1.2 Bond Markets

1.1.3 Loans Markets

1.1.4 Equity Markets

1.1.5 Further Markets

Basic literature:

Mishkin (2012), chapter 2 and parts of chapter 5

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1. Financial Markets1.1 Overview over Financial Markets1.1.1 Asset Market Classifications

(Financial) Asset: Money ⊂ Financial Assets ⊂ All AssetsExamples: Currency, checkable deposits, bonds, stock shares,claims from loan contracts,...

Different assets have different properties:

1. Expected returns (interest rates, dividends, difference in buyingand selling price) – an increase in expected returns makes an assetc.p. more attractive ⇒ demand will increase

2. Risk (returns may have a variance, possible covariance with otherassets) – an increase of risk makes an asset c.p. less attractive ⇒demand will decrease

3. Liquidity (how fast can the asset be sold or used for transactions) –the more liquid the asset is c.p., the more attractive it is ⇒ demandwill increase

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Asset markets: In contrast to goods markets (“producer”,“consumer”) it is possible that an individual or an institution is onthe supply and the demand side.

Economic theory is interested into the questions (e.g.):

I How do different types of agents (e.g. banks, non-banks)structure their balance sheet = how do they behave on thedemand and supply side on the asset markets?

I How can the price movements in aggregated markets beexplained?

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a) Debt and Equity Markets

Debt:

I Contractual agreement, where the borrower pays the holder ofthe asset a fixed amount (interest rate) per period until aspecified expiration date (maturity date). The borrowedamount is returned until (or at) the maturity date.

I The maturity of a debt is the time until the expiration date(short-term < 1 year, long-term > 10 years)

I Examples: Consumer loans/credits, mortgages, bonds

I Depending on the contract, the borrower can sell the asset,especially bonds.

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Equity:

I The buyer of an equity has a claim to share the net incomeand the assets of the seller’s business. The net income is anuncertain residual and is often payed as dividends. Theinstrument has usually no expiration date, hence the funds arenot returned to the holder of the equity.

I Example: Stock shares

I The holder of an equity can sell the asset e.g. on the stockexchange market.

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Advantages and disadvantages:

Debt: Regular payments are more or less certain (unless the debitorstays solvent).

Equity: Residual payments are uncertain. “Residual” means that thefirm has to pay the debitors (and taxes) first.

Debt: In case of insolvency the creditor has a prior claim on theremaining assets.

Equity: Secondary claim on remaining assets in case of insolvency.

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Advantages and disadvantages: (cont.)

Debt: Holder do not profit from increasing profitability andincreasing firm value since their payments are fixed.

Equity: The holder profits directly by higher dividends and increasedvalue of their shares.

Debt: Holder has not the right to vote about management issuesand about the distribution of the net income of the firm.

Equity: Holder has these rights.

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b) Primary, Secondary and Derivative Markets

Primary Market:

I New issues of assets are sold to initial buyers.Examples: firm sells new stock shares or new bonds to aninvestment bank; a bank and a firm sign a loan contract; centralbank issues currencies by open market operations.

Secondary Markets:

I Once an asset has been issued it can be traded at the current price.The transactions are often performed by brokers instead of the assetholders themselves.Example: stock exchange, foreign exchange.

Derivative Markets:

I Not the assets themselves are traded but other claims related to theunderlying assets, e.g. the right to buy a certain asset to a certainprice within a certain period.Example: options, futures. S.14


I Secondary markets make assets more liquid: contract can besold to a current price. Increasing liquidity makes the assetsmore desirable.

I On secondary markets the price is determined by the flow ofinformation as well as by expectations of many agents. Inefficient markets price movements reflect the risk-returnperformance of an asset due to new information. The(expected) price on secondary markets may also affect theprice on the primary market.

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c) Exchanges and OTC Markets (→ secondary markets):

Exchange:

I Organized, centralized, regulated trading of assets, hightransparency of bids, asks and price setting, very competitive,almost arbitrage-free.

Over the counter (OTC):

I Decentralized market where the seller sells the assets “overthe counter” to a buyer. Since OTC dealers are connected bycomputer networks, there is also high price transparency andcompetitivenes, but much less regulation.

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d) Money and Capital Markets:

Money Maket:

I Short-term contracts (maturity < 1 year) with high liquidity

Capital Markets:

I Long-term contracts (maturity > 1 year, assets withoutexpiration date like stock shares)

Note, that this definition of a “money market” differs from theterm as used in macroeconomics where “money” is defined in aspecific manner.

Sometimes “money market” = market for central bank reserves(e.g. interbank market).

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1. Financial Markets1.1 Overview over Financial Markets1.1.2 Bond Markets

Bonds are issued by firms (corporate bonds) or by government(governmental, treasury, municipal bonds).

Two types of bonds:

1. Coupon-bond: owner of the bond receives a fixed paymentper year (coupon rate) until the maturity date. At thematurity date the specified final amount (face vaule, pairvalue) is payed. Special case: perpetuity bond without anexpiration date.

2. Discount bond (zero-coupon bond): There is no couponinterest rate. The bond is sold to a price below the face value.At the maturity date the owner receives the face value.

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Interest rate i when holding the bond until maturity:

P0 =F

(1 + i)n+

n∑t=0

C

(1 + i)t

with P0 = bonds price in t = 0, F = face value, C = coupon rate,n = maturity date.

Expected return r when holding the bond for one period (beforematurity, without discounting):

r =C + Pt+1 − Pt

Pt

where Pt+1 is the expected bonds price in t + 1.

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I In both formulas there is an inverse relationship betweeninterest rate/return and the bonds price!

I If the interest rate is lower than expected return it would beprofitable for all bonds holders to hold the bond only for oneperiod and to sell it in t + 1. Therefore, it can be expectedthat Pt+1 will fall, which results in a decreasing r .

In the opposite case, the holders would decide to hold thebond for a longer time (until maturity). The prices in t + 1will therefore rise until i and r will be equal.

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Slope of demand and supply curves:

I The demand for bonds is negatively related to the bondsprice but positively related to the interest rate i .

I If the interest rate is low and – vice versa – the bonds price ishigh it is more attractive for governments, firms or institutionsto issue bonds to finance their activities. The supply curvecan be assumed to be downward sloped in i . Alternatively, inthe short run the bonds supply can be assumed to beexogenously fixed.

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p price

B

BD

BS

i interest rate

B

BS

BD

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1. Financial Markets1.1 Overview over Financial Markets1.1.3 Loan Markets

Types of loans:

Simple loan: borrowed amount L is paid back plus interestpayment IP at the maturity date n. The interest rate i then solves:

L =L + IP

(1 + i)n

Fixed-payment loan: borrowed amount is paid back includinginterest in fixed payments FP (amortisation plus interest) perperiod until maturity date. The interest rate i then solves

L =n∑

t=1

FP

(1 + i)t

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I Solvency: ability of the borrower to pay back the loan plusinterest.

I Risk: probability distribution for the cases that the borrower isable to pay back α percent of {loan plus interest}; typicalmeasure for risk: variance.

Example: full return (probability p) versus total loss(probability 1− p)

Expected return: r = pi + (1− p)(−1)Variance of return: σ2

r = p(i − r)2 + (1− p)(−1− r)2

(If p = 1 then r = i and σ2r = 0)

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I Borrower has to provide collaterals. The lender can claim thecollateral in case of insolvency.

I In case of mortgages the borrower is not allowed (or it is notpossible) to sell the collateral. The lender has the right toclaim the collateral unless the loan is fully returned.

I There is asymmetric information about p before thecontract (adverse selection problem), and after the contractwhen the loan is used to finance an uncertain project (moralhazard problem). See section 2.3 – 2.4.

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1. Financial Markets1.1 Overview over Financial Markets1.1.4 Equity Markets

I Stock shares as the most common type of equities.I An owner of a stock share has

I claims on the net residual profits⇒ occasionally paid dividends.

I claims on the “firm value”.I What is the “firm value”?

I Net present value of expected cash flow?I Value of the physical and non-physical assets?

I Different models on pricing stock sharesI Problems:

I Expectations depend sensitively on news flow.I Expectations may be driven by less rational determinants

(moods, herding effects etc.)I Expectations are a source of speculation, speculation may drive

the prices, price movements confirm speculation (→ bubbles).

I High volatility of stock prices, high risk.

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1. Financial Markets1.1 Overview over Financial Markets1.1.4 Equity Markets

A case for bubbles? (Dow Jones Index)

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1. Financial Markets1.1 Overview over Financial Markets1.1.5 Further Markets

Options:

I Option contracts are derivatives.I The holder of an option has the right (not the obligation) to

buy or to sell an underlying asset (e.g. stock shares, bonds,foreign exchange, oil, crop,...) to a predetermined price until adefined expiration date.

Buy = call optionSell = put option

I The option itself can be traded. The institution which issuesthe option has the obligation to buy/sell the underlying assetif the holder of an option wishes to exert his right.

I The pricing of options is complicated and is not addressed inthis lecture. The volatility of option prices is high. If the rightis not exercised until the expiration date (this can berational!) there is a 100% loss for the buyer of the option.

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Futures:

I Future contracts are derivates similar to options.

I The main difference is that buyer and seller are obliged toexecute the transaction (and option holder has only the rightto do that).

I The date of transaction is determined in the contract.

Why options and futures?

I Derivative contracts are like “bets” when expectations ofbuyers and sellers are divergent.

I Instrument to incorporate more information into the pricesystem.

I Leverage effect: potential for high profits from speculativederivative contracts.

I Derivatives can be used to hedge risks of the underlying asset.S.29


Foreign Exchange Markets:

I Foreign exchange/currency are also assets.

I Transactions on foreign exchange markets can be caused byunderlying transactions on goods or capital markets (e.g.change sale earnings into domestic currency, demand forforeign exchange in order to pay back a loan).

I Transactions can also be caused by the expectation that thedemanded foreign exchange will appreciate (speculation).

I There are spot markets and future markets for foreignexchange. The latter can e.g. be used for hedging the risks ofan underlying transaction on the goods market.

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1. Financial Markets1.2 Interest Rate Theory

Outline:

1.2.1 Behavior of Interest Rates

1.2.2 Risk Structure of Interest Rates

1.2.3 Term Structure of Interest Rates

Literatur:

Mishkin (2012), chapter 4, 5, parts of chapter 6

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1. Financial Markets1.2 Interest Rate Theory1.2.1 Behavior of Interest Rates

Equilibrium interest rates for bonds changes with demand andsupply on the bonds market:

I Demand shifts by Net Financial Wealth (+), expectedinflation (-), risk (-), liquidity (+) of bonds.

I Supply shifts by changed profitability of investmentopportunities (+), expected inflation (+), governmentalactivities (deficit spending) (+).

Demand = holding bonds as an asset, supply = issuance of bonds

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The role of expected inflation

I Real interest rate = nominal interest rate - (expected)inflation rate (Fisher equation):

i real = i − πe

I Debt contracts specify fixed nominal payments. The real valueof the payments decreases with inflation. This is bad for thecreditor/lender but good for the debitor/borrower(distribution effect of inflation).

I Holding debt assets becomes less attractive, portfolios arerestructured in favor of alternative assets. This leads to anincrease of the nominal interest rates so that real interestrates are not affected by monetary variables (Fisher effect).

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i

B

BS0

BD0

BD1

BS1

πe ↑ ⇒ i ↑

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Source: Mishkin (2010)

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1. Financial Markets1.2 Interest Rate Theory1.2.2 Risk Structure of Interest Rates

Risk: (details in Bailey (2005), chapter 4)

I Realized returns r are uncertain, they are dispersed around amean E [r ]. Risk measured here by Var [r ].

I Agents can assumed to be risk averse = utility function isconcave in returns: u′(r) > 0, u′′(r) < 0.

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Risk premium:

I Given a return rs of a risk-free/safe asset (so-called certaintyequivalent). Which risk premium RP on the risk-free return isrequired so that the expected utility of the return r of a riskyasset equals the utility of the risk-free asset? In other words:which RP is necessary in order to make an investor indifferentbetween holdung the risky or the safe asset?

I No-arbitrage condition:

u(rs) = E [u(r)]

I Note that in general it is E [u(r)] 6= u(E [r ]) (except for alinear function u)! We define

E [r ] = rS + RP

such that u(rs) = E [u(r)] holds true (with RP > 0 in case ofconcave u(·)).

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u(r)

r (return)p(r)

r

u(E [r ])

E [r ]

E [u(r)]u(rs) =

rs

RP

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u(r)

rrL rH

Case (a): p(rL) = 0.5, p(rH) = 0.5

Ea[r ]

Ea[u(r)]RPa

Case (b): p(rL) = 0.2, p(rH) = 0.8

Eb[r ]

Eb [u(r)]RPb

Note: E [u(r)] =∑

i p(ri )u(ri ) or =∫p(r)u(r)dr

u(r)

rp(r)

r

rB

Ea[u(r)]

Ea

RPa

Eb [u(r)]

Eb

RPb

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Relation between risk premium and risk (variance):

I The risk premium increases with the risk (Var [r ]) of theuncertain return. It can be shown that

RP ≈ −u′′(r)

u′(r)︸︷︷︸ARA

·Var [r ]

where ARA is the so-called Arrow-Pratt measure of absoluterisk aversion (measuring the “concavity” of the utilityfunction).

Risk premia for bonds:I Fixed payment contract: investor has claims rB .I Default means that r < rB is realized with a certain

probability (see previous graphic)I It follows E [r ] < rB .

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u(r)

rrs

u(rs)

p(r)

r

rB

E [u(r)] =RPb

E [r ]

spread

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Risk premia and interest rate spreads:

I Risk premia are not directly observable but the resultinginterest rate differences are.

I Assume a safe bond with (effective) interest rate rs .I A risky bond with (effective) interest rate rB has an expected

return E [r ] < rB .I According to subjective risk aversion investors demand bonds

such that no-arbitrage condition holds true: RP = E [r ]− rs .⇒ resulting interest rate differentials (spreads) rB − rs .I Spread is linked to the risk premium: increasing spreads

indicate increasing risk premia.

Consequences:

I Corporate bonds are perceived as riskier than sovereign bonds.I The worse the rating (AAA, AA, B+, ...) the higher the risk

and the higher the interest rate.S.42


Case (a): both bonds are perceived as safe (same i)

i

treasury bonds

Bs

Bd

Case (b): corporate bonds are now perceived as risky

Bd1

i

corporate bonds

Bs

Bd

Bd1

spread

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source: Mishkin (2010)

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source: German Council of Economic Experts

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In addition: Liquidity premium

I How easy is it to find a counterparty on the market who iswilling to buy the asset at the current market price?

I The more illiquid an asset is, the higher the interest rate inorder to compensate this disadvantage (again, a no-arbitragecondition).

I Bank loans are typically not very liquid compared to bonds orstock shares.

I Securitization of loans (Asset Backed Securities): financialinstrument making loans more liquid.

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1. Financial Markets1.2 Interest Rate Theory1.2.3 Term Structure of Interest Rates

Yield Curve:

Describes the term structure of interest rates for bonds of a giventype (with identical risk and liquidity characteristics) or for abundle of bonds.

I Upward sloping yield curve (“normal yield curve”): long-terminterest rate above short-term interest rates

I Downward sloping yield curve (“inverted yield curve”): viceversa

I Flat yield curve: same interest rate in short and long run

I (Inverted) U-shaped yield curve etc.

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i

residual maturity (years)

normal yield curve

flat yield curve

inverse yield curve

(Daily and historical yield curves can be interactively calculated on the ECB’s

home page.)

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Stylised empirical facts:

1. Interest rates of bonds with different maturities move jointly.

2. If the short term rate is low it is likely that yield curve isupwards sloped; vice versa if the short-term rate is high.

3. The upwards sloped yield curve is the typical case.

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Expectations Theory

I Assume that short-term rate is low. Agents expect increasingeconomic activity (productivity, profitability, but also inflationincrease). Therefore the demand for funds to financeadditional investments will increase. The expected interestrate level will rise (= falling bonds prices). If you buy along-term bond today, the expected higher short-term interestrates in the future have to be reflected in the currentlong-term interest rate.

I Explains the first two stylised facts but not the third one.

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Example: One Euro is invested for two periods.

Buying one long-term contract or subsequently two short-termcontracts?

Rlong = (1 + i0,2)2

Rshort = (1 + i0,1)(1 + i1,1)

where ij ,k is the interest rate at time j for a k-period contract.

In an arbitrage-free market we have Rlong = Rshort which implies

i0,2 =√

(1 + i0,1)(1 + i1,1)− 1

where i1,1 is the expected short-term rate. The current long-terminterest rate is the geometric mean of the current and the expectedshort-term interest rate in the future.

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If expectations are not systematically false, there should be acorrelation between the slope of yield curves and the businesscycle: before a cyclical downturn the yield curve will become flat orinverted. Before an economic recovery the slope of the yield curvewill rise.

Empirical Literature:

Bernhard, H., Gerlach, S. (1998), Does the Term Structure PredictRecessions? The International Evidence. International Journal ofFinance and Economics Vol. 3(3), 195-215.

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Segmented Markets Theory:

I Long- and short-term bonds are not close substitutes.

I Investors have different preferences for different maturities.

I Bonds are traded in different (segmented) markets.

I It seems to be plausible that investors prefer short-termmaturities which would explain the stylised fact 3 but not fact1 and 2.

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Liquidity Theory:

I Bonds of different maturities are (imperfect) substitutes⇒ expected returns correlate like in expectations theory.

I Investors prefer short-term maturities so that short-termmarkets are more liquid. Buying a less liquid bond requires a“liquidity premium”.

I Since this incorporates the expectations theory, all threestylised facts are explained.

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Monetary Policy:

I As it will be discussed later on, the central banks try toinfluence the long-term interest rate.

I The conventional policy tool, the main refinancing (moneymarket) rate, however, is short-term ⇒ transmission tolong-term rates.

I Unconventional measures like buying massively long-termgovernmental bonds (QE).

I “Forward Guidance”: promise to keep short-term rates verylow also in the future.

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2. Theory of Financial Structure2.1 Financial Intermediates

Outline:

2.1.1 Economic Functions of Financial Intermediates (FI)I Asset TransformationI Reducing Transaction CostsI Risk SharingI Dealing with Asymmetric Information

2.1.2 Types of Financial Intermediates

Literature:

Mishkin (2006), chapter 2

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2. Theory of Financial Structure2.1 Financial Intermediates2.1.1 Economic Functions of Financial Intermediates

Provider:

1. Households2. Firms3. Government4. Foreign

Receiver:

1. Households2. Firms3. Government4. Foreign

Market

FinancialIntermediates:

1. Banks2. Funds3. etc.

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a) Asset Transformation:

(Note that liabilities of the intermediate = asset of the houshold or firm)

I Lot size transformation:e.g. many small deposits, few large credits

I Maturity transformation:short run liabilities, long-run assets

I Risk transformation:e.g. less risky liabilities, more risky credits (see below)

I Liquidity transformation:high liquid liabilities, less liquid assets

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b) Reducing Transaction Costs:

I FI have economies of scale:

getting information about demanded and provided funds,assessing risks, bargaining, designing and enforcing contracts,buying/selling stock shares – these tasks can be accomplishedby FI with much lower transaction costs due to specializedinformation processing abilities, large transaction volumes,specific human capital (expertise).

I FI have economies of scope:

FI provide additional services like risk diversification,optimizing portfolios, and consulting. Sometimes theseservices need the same infrastructure and the same humancapital. Hence it may reduce cost when one FI provides theseservices.

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c) Evaluating, Pooling and Allocating Risk:

I Risk: e.g. investment projects may fail, borrowers may becomeinsolvent.

I Evaluating risks ⇒ calculating risk premia.

I Reducing the risk by pooling and diversification.

I Transforming the risk structure of financial assets.Examples:

I Depositors hold “safe” asset and receive low interest rates.Bank provide risky loans with high interest rates (including riskpremia).

I Securitization of risky loans and selling them ⇒ changes assetstructure and re-allocates the risk.

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d) Dealing with Asymmetric Information (see 2.3 – 2.4)

I Adverse Selection:I Hidden characteristics of a potential borrower before

contracting.I Borrower knows his risk better than the lender.I If lender offers a contract which is optimal for a borrower with

average risks, this may be unattractive for those with goodrisks. This may result in a market failure.

I Moral Hazard:I Hidden action of a borrower after contracting.I Borrower takes the money to engage in a prject that is

undesireable for the lender. This reduces the probability for asuccessfully returned credit.

I FI may mitigate this problem e.g. by screening, collaterals,optimal design of contracts. Again, they have the resources todo that at low transaction costs.

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2. Theory of Financial Structure2.1 Financial Intermediates2.1.2 Types of Financial Intermediates

Depository institutions (banks):

I Accept deposits from individuals and institutions as liabilities,providing loans and mortgages as assets.

I Example: Commercial banks.

Contractual savings institutions:

I Accept premiums and contributions from government, firmsand individuals as liabilities, investment in bonds, stocks andgovernment securities.

I Example: life insurance, retirement funds.

Investment intermediates:

I Selling commerical stocks, bonds or shares as liabilities,providing business loans and investment in stocks and bondsas assets.

I Example: Finance companies, private equity funds.S.62


Type of FI Primary Liabilities Primary Assets ValueDepository Institutions

Commercial Bank Deposits Loans, mortgages,bonds 12,272

Saving/loan associations Deposits Mortgages,and mutual saving banks consumer loans 1,518

Contractual saving Institutions

Life Insurance Companies premiums Bonds, mortgages 4,798Fire/Caaualty Insur. Comp. premiums bonds, stocks 1,337Pension funds employer/employee bonds, stocks

contributions 5,193Gov. retirement funds employer/employee bonds, stocks

contributions 2,730

Investment Intermediates

Finance Companies commercial papers, loansstocks, bonds 1,910

Mutual Funds issued shares bonds, stocks 6,538Money market mutual funds issued shares money market instr. 3,376

(US Data 2008 , Bill. Dollar; source: Mishkin (2010), Tables 3 and 4, data from Federal Reserve)S.63


Non-bank Financial Intermediaries (NBFI) are sometimes called“shadow banks”

I Risk originators:I Depository institutions (commercial bank 6∈ NBFI)I Broker dealer (investment banks)I Finance companies

I Risk bearers:I Managed funds (insurance companies, retirement funds etc.)I Institutional investors (mutual funds, money market funds,

hedge funds)

I Special Purpose Vehicles (intermediary institution for thesecuritization process)

Poschmann, J. (2012), The Shadow Banking System – Survey and Typological

Framework. Global Financial Markets Working Papers No.27, Jena/Halle.

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Why do NBFI exist?

I Specialisation on transactions where no deposits are involved.

I Financial intermediation combination with different privategoods (e.g. insurance).

I Regulatory arbitrage: Banks are highly regulated, but“shadow banks” are much less regulated ⇒ they can do riskyinvestments to less costs. But: no access to short-run centralbank liquidity and “safety nets” like deposit insurance.

I Utilized also by banks e.g. by securitization and selling theclaims from loans to NBFI.

S.65

2. Theory of Financial Structure2.2 Portfolio Selection and the Management of Return, Risk and Liquidity

Outline:

2.2.1 General Principles of Bank Management

2.2.2 Theory of Portfolio Selection

2.2.3 The Value at Risk Approach

Literature:


Bailey (2005), chapter 5

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2. Theory of Financial Structure2.2 Portfolio Selection and the Management of Return, Risk and Liquidity2.2.1 General Principles of Bank Management

The Bank’s Balance Sheet

Assets LiabilitiesI Reserves (required, excess)

I CashI Securities/Bonds

I firm bondsI governmental bonds

I LoansI industrialI consumerI real estateI inter-bankI other

I Other assets(e.g. physical assets)

I (Checkable) Overnightdeposits

I Nontransaction despositsI Time depositsI Redeemable deposits

(saving accounts)

I BorrowingsI Inter-bank loansI Central bank loansI Other

I Bank Capital / Net WorthS.67


a) Liquidity Management

I Liabilities are stochastic (sudden inflows/outflows of deposits)⇒ need for liquid assets like cash or reserves.

I If there are not enough liquid assets, the bank needs expensiveovernight loans, or has to sell other assets (“fire sales”), or itbecomes illiquid.

I Problem: If customers receive a signal of possible liquidityproblems, they wish to draw their deposits. This enforces theliquidity problem and may induce bankruptcy (bank runequilibrium, see Diamond/Dybvig model).

I Given a probability distribution of inflows and outflows on theliability side, the asset side should consist of enough liquidassets to meet the obligations to the depositors and creditors.

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Role of the Interbank market

I Most transactions are deposit transfers from bank A to bank B.Bank A is then in need for liquid reserves while bank B has excessliquidity.

I Interbank market for “clearing” the demand and supply of liquidreserves by short-run interbank loans (often called money market).

I The money market interest rate is the primary operative goal of thecentral bank policy.

I What happens if banks do not supply excess liquidity on theinterbank market, e.g. because of distrust to other banks or fear ofliquidity distress? ⇒ increased central bank loans; central bank aimsto avoid liquidity problems in the banking sector.

I Financial crisis 2008/2009 (and also later): drastically increasedcentral bank loans but also drastically increased excess reserveholding at the central bank.

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Money transfer from bank A to bank B:

(1) Initial situation

Bank A Bank BAssets 500 Deposits 500 Assets 500 Deposits 500Reserves 50 CB loans 20 Reserves 50 CB loans 20

Capital 30 Capital 30

(2) Money transfer ∆ Deposits = ∆ Reserves = 50 units from A to B


Capital 30 Capital 30

(3) Bank B lends reserves back to bank A


IB loans 45 IB loans 45Capital 30 Capital 30S.70


Frictions on interbank market:

I As most of deposit withdrawls are transfers between banks,sudden deposit (and reserve) outflows at A means that thereare sudden deposit (and reserve) inflows at B. So it should bepossible that excess demand and excess supply of reserves“net out” by interbank lending.

I In case of market frictions (e.g. banks have limited trust toeach other, want to keep more reserves etc.):

I Banks could hold more reserves and other highly liquid assetsin order to “secure” against liquidity problems due to interbankmarket frictions (see below: “Liquidity at Risk” approach)

I Banks could fire-sale oher assets (expensive).I Banks could demand central bank loans (where overnight loans

are also expensive).

S.71


b) Asset Management

I Management of risk and return of the assets. Investing into amix of risky and riskless assets with the highest expectedutility (portfolio approach). But: portfolio approach requiresassumption of risk aversion which is empirically questionable.

I Restrictions to asset management:I Liquidity considerations: The need for sufficient liquiditiy is a

restriction for asset management.I Capital regulation (Basel II/III): value of rsiky assets is risk

weighted, capital requirements for these risk weighted assets.

This prevents from holding too many too risky assets.

⇒ Incentive for securitization

S.72


Excourse: Securitization

I Illiquid assets like loans are pooled to a specific portfolio.

I This portfolio is transferred to an entity called SpecialPupose Vehicle (SPV).

I The SPV securitizes this portfolio and issues rated AssetBacked Securities e.g. to funds, and receives liquid assets inexchange which are transferred back to the bank.

I From the bank’s perspective, and illiquid asset is thereforetransformed into a liquid asset. The risk of the underlyingsecurities is transferred to the fund (and fund share holders).Although the amount of issued risky loans is the same asbefore, the bank has a better loans/capital ratio.

I Different types of securitization and ABS (not discussed here).

S.73


c) Liability management

I Deposits are not “given” and not the only source of liquidity.Decision how to aquire which types of liabilities.

I Differences of liabilities:I Hows fast could an additional liability be aquired?I Probability of outflowsI Differences in maturityI Costs = interest rates (e.g. for time deposits, for inter-bank or

central bank loans)

I Development of new financial instruments (e.g. certificates ofdeposits (CD) which are similar to bonds)

S.74


Remark: Why do banks need deposits?

I The view that banks attract financial resources (e.g. deposits)which are then lend out to investors, is very old-fashioned,more precisely: misleading, even more precisely: wrong !

I As can be seen in ch. 3, deposits are created by issuing loans,therefore they cannot pre-exist before loans are issued.

I However, once when loans and thus deposits are created, thenewly created deposits will typically be transferred to anotherbank. (Nobody demand loans to keep the money on a bank deposit.)

I Thus banks need enough reserves when creating loans. Thiscan be done e.g. by attracting deposits.

S.75


d) Bank Capital Management

I Most assets have risks: Credits may fail, bonds prices may fall.Hence, the value of the asset side is under risk of beingdepreciated.

I With a certain probability the losses of the asset side mayexceed the bank capital: the bank becomes insolvent.

I Trade-off : More risky investments enlarge the return onequity capital, but also the risk of insolvency!

I This is regulated by Basel II / III (see above)

S.76

2. Theory of Financial Structure2.2 Portfolio Selection and the Management of Return, Risk and Liquidity2.2.2 Theory of Portfolio Selection

Outline of Portfolio Theory

(Bailey (2005), chapter 5)

I We address the case of two risky and one risk-free asset.

I Notation:

µi expected return of risky asset i = 1, 2σ2

12 covariance between the returns of asset 1 and 2σ2ii variance of returns of asset i = 1, 2

ai proportion of portfolio invested in asset i ,∑

i ai = 1r0 return of the risk-free asset

I Idea: investing into a pool of risky assets could create a betterrisk-return combination than each single asset.

S.77


i) Properties of the portfolio P

For P we have

µP =∑i

aiµi (1)

σ2P =

∑i

∑j

aiajσ2ij (2)

In case of two risky assets the proportion a1 (obviously a2 = 1− a1)determines the expected return and the variance of the portfolio.

S.78


ii) Efficiency Frontier

I In case of more than two risky assets the convex set ofproportions a1, ...an define a convex set of(µP , σ

2P)-combinations.

I Most of these combinations are inefficient, since there existmany portfolios with the same µP but different σ2

P .

I In the first step, the efficiency frontier has to be derived byminimizing σ2

P (over ai = 1, ...n) under the constraints ofgiven µP = µP and

∑i ai = 1

I In case of two risky assets, this step is not necessary since aidetermines a unique (µP , σ

2P)-combination.

S.79


The shape of the efficiency frontier EF depends on the covariance

(ρ12 = σ212/(σ1σ2) is the correlation coefficient).

µP

σP

Asset 1

Asset 2

with ρ12 = 1

with ρ12 = −1

with ρ12 ∈ (0, 1)

E

F

S.80


iii) Optimal portfolio without a risk-free asset

I From the set of efficient portfolios choose the optimalportfolio wich maximizes expected utility function.

I Mean-Variance-Approach:

maxai

E [u(rP)] = µP − θσ2P with

∑i

ai = 1

with θ > 0 as the degree of risk aversion.Recall that µP , σ

2P depend on ai .

Note: This is a very special type of utility function with some unfavorable

feautures. One should prefer general approaches from EUT.

I In a (µP , σP)-diagram the indifference curves are upwardssloped. The tangential point (R) of the indiffrenece curve withthe efficient portfolio frontier is the solution of theoptimization problem.

S.81


µP

σP

Asset 1

Asset 2

indifference curves

R

optimal portfoliowithout risk-free asset

S.82


iv) Optimal portfolio with a risk-free asset

I The riskless asset has a return r0 and zero variance.

I The risky portfolio Z is a mix of two risky assets with

µZ = λZµ1 + (1− λZ )µ2 (3)

σ2Z = λ2

Zσ21 + (1− λZ )2σ2

2 + 2λZ (1− λZ )σ212 (4)

⇒ σZ =√λ2Zσ

21 + (1− λZ )2σ2

2 + 2λZ (1− λZ )σ12 (5)

where λZ has to be determined in an optimal way. Theresulting portfolio Z must lie on the efficiency frontier.

S.83


I If portfolio Z is then mixed with the riskless asset (share λP).The resulting portfolio P has the properties:

µP = λP r0 + (1− λP)µZ (6)

σ2P = (1− λP)2σ2

Z (7)

⇒ σP =√

(1− λP)2σ2Z = (1− λP)σZ (8)

Thus, the risk and return of P is a linear combination of Zand the riskless asset.

S.84


I In a (σ, µ)-diagram we can therefore write(see also the figure):

µP = r0 + bσP (9)

= r0 +

(µZ − r0σZ

)σP (10)

µP

σP

Z

slope br0

µP

σP

Asset 1

Asset 2

r0

Z

Maximizing slope bsubject to efficiency frontier

⇒ optimal risky portfolio Z

S.85


How to determine the risky portfolio Z?

I Note, that an optimal portfolio P will be a tangential pont ofthe indifference curve with the linear function (9).

I Every point on a steeper linear function (9) dominates thepoints on a flatter linear function since we obtain a higherreturn with the same standard deviation.

I Therefore, we maximize the slope b = (µZ − r0)/σZ withrespect to λZ under the condition that µZ , σZ are definedaccording to (3) and (5). This guarantees that Z lies on theefficiency frontier.

I Obviously, Z must be a tangential point on the efficiencyfrontier!

S.86


maxλZ

b =µZ − r0σZ

s.t. (3), (5)

⇒ λ∗Z =(µ1 − r0)σ2 − (µ2 + r0)σ12

(µ1 − r0)σ2 + (µ2 − r0)σ1 + 2r0σ12 − (µ1 + µ2)σ12

I Now the optimal risky portfolio Z is determined. The linearequation (9) with λ∗Z (and henceforth b∗) is called CapitalAllocation Line (CAL).

I Now, the optimal mix between Z and the riskless asset isdetermined as usual as the tangential point of the indifferencecurve with the CAL. The solution depends on the degree ofrisk aversion.

I Note, that irrespective of the individual risk aversion, allrational investors will choose the same risky portfolio Z(Tobin separation).

S.87


µP

σP

Asset 1

Asset 2

r0

Z

capital allocation line

P

P = optimal portfolio with

two risky assets

and one risk-free asset

S.88


Analytical solution:

µP = λP r0 + (1− λP)µZ (11)

σ2P = (1− λP)2σ2

Z (12)

It follows for the utility function

maxλP∈[0,1]

u(µp, σ2P) = µP − θσ2

P

= λP r0 + (1− λP)µZ − θ(1− λP)2σ2Z (13)

From FOC we have for the risky share:

1− λP =µZ − r0

2θσ2Z

S.89


Possible extensions:

I Applying more general classes of utility functions (e.g. withconstant Arrow-Pratt measures of risk aversion).

I Applying additional constraints (e.g. minimum expectedportfolio returns, maximum probability of tolerated losses ⇒see VaR approach below, etc.)

I Allowing for “short sales” (negative shares of an asset).

S.90


Limitations:

I Risky assets have to be backed by capital (see VaR approachbelow, also bank regulations like Basel II/III)

I The bank needs a certain liquidity of their assets. Liquidity isnot addressed in the portfolio approach (see below).

I Banks have to hold specific securities as a collateral in orderto have access to Central Bank credits.

⇒ These things are constraints to the Portfolio Approach.

I Empirically seen, there is not much risk aversion.

S.91

2. Theory of Financial Structure2.2 Portfolio Selection and the Management of Return, Risk and Liquidity2.2.3 The Value at Risk Approach

Now we turn back to solvency and liquidity managementconsiderations.

I Once the optimal portfolio is determined, the value of theassets is uncertain: bad loans have to be written off, bondsprices may fall etc. ⇒ the value of the assets is a stochasticvariable.

I For a given period (e.g. 1 month) it is possible to construct aprobability distribution F for the losses of value (wherenegative losses are gains).

I Bank management (or the regulation authority) wishes that inthe given period the bank stays solvent with a probability of1− α%. Then the upper α-percentile of the distribution Fdenotes the losses – the VaRα benchmark – which can beexpected with probability of α%.

S.92


VaRαgains losses

F

probability α%

probability (1− α)%

S.93


I In order to stay solvent with probability 1− α% within thisgiven period (means that we tolerate insolvency probabilityα%), the bank has to keep bank capital which covers (atleast) the VaRα benchmark: BC ≥ VaRα.

I When VaRα is determined, then rα denotes the percentage ofthe asset volume A which will be lost with probability α:

VaRα = rαA

⇒ BC

A≥ rα

so we say that rα% of the assets are backed by capital.

I If BC ≥ r0.02A then losses which exceed bank capital(insolvency) have a probability less than 2%.

S.94


Some problemss with the VaR concept:

I Risk measures should meet some desirable properties (not tobe discussed here). The VaR measure is e.g. not coherent:calculating the VaR for two risky portfolios, the VaR for thejoint portfolio should be lower than the sum of the singleVaRs due to the pooling/diversification effect. However, theVaR measure cannot guarantee that.

I No information about the expected losses in case of insolvency(e.g. two portfolios might have the same VaR measure butdiffer in case of extraordinary large losses).

I Assumption of normal distribution is questionable.I Assumption that past experiences, as expressed in the

distribution F , also hold true for the future, is questionable,especially for long-run considerations(⇒ “stress tests” as an alternative).

S.95


Applying VaR to Liquidity Management:Liquidity at Risk

I Consider a liquid asset (e.g. reserves) and stochastic depositsD. Liquidity management should ensure that bank stays liquidwhen depositors wish to withdraw their deposits.

I The VaR approach can also be applied to this task: Let G bethe pobability distribution of daily deposit net outflows (wherenegative net outflows are net inflows). Then β is the tolerableprobability that the outflows exceed the reserves and the bankgets into liquidity troubles.

I Hence the deposits D should be backed by reserves R suchthat R ≥ rβ · D, e.g. 5% of the deposits should be backed byreserves. (Recall, that the obligatory required reserve rate isonly 1%).

S.96


I It has to be noted that the “Liquidity at Risk” approach is anadditional constraint for the portfolio management: Theshare of the most liquid asset (e.g. excess reserves) isdetermined by the degree of risk aversion of the bank but isalso restricted by the VaR approach.

I Summing up: The bank makes simultanous complex decisionsabout the volume and the structure of the asset and theliability side.

Linsmeier, T.J., Pearson, N.D. (2000), Value at Risk. Financial Analysts

Journal 56(2), 47-67.

S.97

2. Theory of Financial Structure2.3 Adverse Selection Problems

Outline:

2.3.1 Introduction

2.3.2 How Adverse Selection Influences Financial Structure

2.3.3 Solutions: Screening, Signalling, Regulation, Collaterals

2.3.4 What Stylized Facts are Explained by Adverse Selection?

Literature:


Wolfstetter, E. (1999), Topics in Microeconomics, chapter 9

S.98

2. Theory of Financial Structure2.3 Adverse Selection Problems2.3.1 Introduction

Information Asymmetries:

I Principal: offers contract, lack of informationI Agent: signs contract, private information

Before contracting: hidden characteristics → adverse selection

I buying shares or bonds of a firm ⇒ characteristics are notknown to the buyer

I providing a loan to a borrower with unknown ability to payback the loan (credit risk)

⇒ Principal’s expectations are built on limited information aboutcharacteristics

⇒ Principal’s decision is based on these expectations

⇒ limited possibilities to reveal the unknown characteristics

⇒ Pooling vs. Separating equilibria

S.99

2. Theory of Financial Structure2.3 Adverse Selection Problems2.3.2 How Adverse Selection Influences Financial Structure

After contracting: hidden action → moral hazard

I Agent uses the funds for financing projects which are morerisky than announced to the principal, or he reduces themanagerial effort because this might enhance his benefits.

I Principal cannot observe this, but he can expect that there isan incentive for moral hazard.

I Optimal design of the contract in order to mitigate or avoidMH.

S.100


Markets for Lemons

I Akerlof, G.A. (1970), The Market for Lemons: QualitativeUncertainty and the Market Mechanism. Quarterly Journal ofEconomics Vol. 84, 499-500.

I Wolfstetter, E. (1999), Topics in Microeconomics. (Chapter9.2.1)

Nobel Prize 2001 to George A. Akerlof, A. Michael Spence, JosephE. Stiglitz

”for their analyses of markets with asymmetric

information“.

Foundation of market imperfections or market failures due toinformation asymmetries.

S.101


The original version: Market for used cars

I Cars have a different quality q (from “very good” q = b to“bad” q = 0, bad cars = “lemons”)

I The seller is privately informed about the quality q ∈ [0, b].

I The seller will accept any price p ≥ q.

I The buyer is willing to pay any price p ≤ α · q with α > 1.

I For any given q there exists a price ∈ [q, αq] where buyer andseller mutually benefit from the deal.

I But: The buyer is not able to observe q⇒ building expectations E [q].

S.102


Assume that the quality q is uniformly distributed on [0, b]. This isknown by the buyer. For any used car the expected quality is henceE [q] = b/2. Therefore

p(E [q]) ≤ α · b2

Two cases:

I Case 1: α ≥ 2. Then the buyer is willing to pay p ≥ b and allcars will be sold.

I Case 2: 1 < α < 2. Then the market breaks down!

S.103


Market breakdown:

I For α < 2 the buyer will never pay p = b.

I No high quality cars (q = b) will be sold. They can be removedfrom the interval (e.g. q ∈ [0, b − ε]).

I This can be anticipated by the buyer. The expected average qualitydecreases (e.g. E [q] = (b − ε)/2).

I The willingness to pay also decreases.

I The remaining best quality cars leave the market.

I and so forth... (“race to the bottom”)

S.104


Or in another way:

I Assume an arbitrary merket price p > 0. Obviously there areonly sellers i the market with qi ∈ [0, p]. The average quailityis hence E [q] = p

2 .

I This is known by the buyers. The are willing to pay maximump(E [q]) = α/2 · p.

I For α < 2 this is lower than the market price and no dealcomes about.

Mutually beneficial contracts are not realized⇒ Pareto inefficiency!

S.105


Financial Markets:

I Firm needs funds to finance a risky project. Assume that thefirm demands for a loan L.

I The firm is willing to pay an interest rate iL which does notexceed the expected return of the project r .

I The bank will provide the loan L when the interest rate coversat least the interest rate for a secure asset iS plus the riskpremium RP (more precisley: we mean the spread).

I Assume that the loan is either returned successfully withprobability 1− p or it fails completely with probability p. Theminimum risk premium is therefore:

L(1 + iS) = L(1 + iL)(1− p) + 0 · p (14)

⇒ RP = iL − iS =p

1− p(1 + iS) (15)

S.106


I Problem: p is private information of the firm!

I Offering a loan contract with an interest rate iL (incl. riskpremium) based on the expected probability E [p] taken froma prior distribution of risks.

I Typically the expected return and the risk of investmentprojects are positively correlated. Firms with profitable lowrisk projects with

r < iS +E [p]

(1− E [p])(1 + iS)

will not have in incentive to sign a loan contract!

I The remaining projects are hence more risky which leads toan increase of E [p] ⇒ a similar mechanism as in the “marketfor lemons” example applies.

S.107


Credit Rationing:

Stiglitz, J., Weiss, A. (1981), Credit Rationing in Markets with Imperfect

Information. American Economic Review 71, 393-410.

Adverse Selection Effect: With an increasing interest rate more andmore good (= low risk) projects leave the market and the expectedrisk increases:

E [p] = E [p(iL)],dE [p(iL)]

diL> 0

S.108


Profit maximizing bank: (L given)

maxiLπ = (1− E [p(iL)])(1 + iL)L (16)

⇒ dπ

diL= −dE [p(iL)]

diL(1 + iL)L + (1− E [p(iL)])L = 0

(17)

⇒ i∗L =(1− E [p(iL)])− dE [p(iL)]

diLdE [p(iL)]

diL

(18)

profits

iLi∗L

S.109


Consequences:

I The profits do not monotonously increase with market interestrate iL but are hump-shaped, as Stiglitz/Weiss conclude.

I If loans demand increases, there is not necessarily a Walrasianadjustment of the equilibrium interest rate!

I The demand side of the loans market will be rationed.

I Existence of rationing equilibria.

I Capital market inefficiency also plays a macroeconomic rolebecause the problem affects e.g. investment plans.

S.110


The Stiglitz/Weiss (1981) model has been very influential but isalso criticized:

I Arnold/Riley (2009) show that even taking the very specialassumptions of Stiglitz/Weiss seriously, one cannot derive ahump-shaped revenue curve. Multiple equilibria might occurbut rationing sitauations are not very likely.

Arnold, L.G., Riley, J.G. (2009), On the Possibility of Credit Rationing in

the Stiglitz-Weiss Model. American Economic Review 99(5), 2012-2021.

I There are different views on the role of collaterals which couldreduce risk premia and thus adverse selection effects.Moreover, they can serve as a selection device (Bester 1985,see below).

I However, it is generally accepted that information asymmetriesmight lead to market frictions, also on financial markets.

S.111

2. Theory of Financial Structure2.3 Adverse Selection Problems2.3.3 Solutions: Screening, Signalling, Regulation, Collaterals

There are different ways how to solve or to alleviate the problem:

I Providing better information = decreasing informationasymmetry

I Screening: The less informed agent has an incentiveI to collect information by himselfI to buy additional information supplied by other agentsI to provide different contracts with self-selection effects

I Signalling: The privately informed agent has an incentive toprovide a trustworthy (costly) signal about his characteristics.

I Governmental Regulation

I Collateral

The information asymmetry is not necessarily resolved but hasminor consequences since in case of a failed project the returnof the loan is backed.

S.112


Screening by collecting information

I High information costs, especially for lenders with lowexpertise.

I Bank as a financial intermediate with expertise and specializedhuman capital reduces such information costs: screening costsof multiple non-specialized lenders are reduced and transferredto the bank.

I The existence of a professional banking system is aprerequisite for a working credit market.

S.113


Screening by buying information provided by others

I Rating agencies (e.g. Standard & Poors, Moody): (large)borrowers are rated according to a standardized scale (seeMishkin (2006))

Problems:

I Free-rider problem since information is a non-rival good.Once, when information is made public, there is no incentiveanymore to pay for it.

I How trustworthy is that information? RA typically payed bythe better informed party. Less informed party is not able toassess the reliability of the information ⇒ Moral Hazardproblem.

S.114


Screening and self-selection (separating equilibrium):

I Bester, H. (1985), Rationing in Credit Market with ImperfectInformation. American Economic Review 75, 850-855.

I Besanko, D., Thakor, A. V. (1987), Collateral and Rationing: SortingEquilibria in Monopolistic and Competitive Credit Markets. InternationalEconomic Review 28, 671-689.

I High/low risk investors with probabilities of default pH > pLwhere pj is private information (j ∈ {H, L}).

I Bank offers two types of contracts: (iL,CL > 0) and(iH ,CH = 0) with Cj as the collateral per unit of borrowedcapital.

S.115


I For a high risk investor it is more likely that he will have topay the collateral. Both investors compare the expected costs:

(1− pj)iL + pjCL ≷ (1− pj)iH

⇒pj

1− pj≷

iH − iLCL

Since the l.h.s. is larger for the risky investor than for low-riskinvestors, there exists combinations of (iL, iH ,CL)(determining the r.h.s. of the equation) such that theinequality sign is different for both investor types.

⇒ Investors will choose different contracts and therefore revealtheir type (separating equilibrium)!

S.116


Governmental Regulation:

If investors need financial funds, e.g. by demanding credits orselling bonds or stocks, they can be forced by law to provide someinformation to reduce the information asymmetry. E.g.

I adhere standard accounting principles

I providing information about the balance sheet and other(financial) indicators like sales, earnings, assets

I in case of stock markets: publish relevant informationsregularly; annual meeting of shareholders etc.

S.117


Signalling:

I A firm with a low risk project has an incentive to provide asignal so that the lender is informed about the low risk.

I If signalling should make sense...

(a) the signal must be costly(b) there must exist signals that are too expensive for a high risk

firm but not too expensive for low risk firms⇒ discrimination is possible.

I Otherwise high risk firms have an incentive to imitate thesignal so that signalling provides no information (poolingequilibrium).

S.118


Signalling means “building reputation”.

Reputation signals (e.g.):

I Loans have been successfully returned in the past.

I Projects are financed also with equity capital.

I Firm provides voluntarily more sensitive information thanrequired by law.

I Firm has valuable assets (→ similar to collaterals).

This may be a problem for new and small firms.

S.119


Collaterals:

I In case of failure of the investment project the investor hasother assets which can be sold to meet the debt obligations.

I Borrower must prove that he has such collaterals beforesigning the credit contract.

I Credit contract includes the obligation that the collateralmust not sold until the credit is returned successfully.

I Cedit contract includes that lender automatically becomes theowner of an asset in case of a credit failure.

I In some contracts, the lender has property rights on the assetwhich is financed by the credit. These property rights arereturned to the borrower in case of a successfully returnedcredit ⇒ mortgages (e.g. in case of housing)

S.120


Collaterals C lower the risk premium:

L(1 + iS) = L(1 + iL)(1− p) + pC (19)

⇒ RP = iL − iS =p

1− p(1 + iS)− p

1− p

C

L(20)

with C ∈ [0, (1 + iS)L]. In case of C = L(1 + iS) there is no creditrisk for the lender any more.

Problems:

I Providing collaterals and liquidation is costly.

I The access to collaterals is limited (e.g. start-up companies).

I The value of collaterals is uncertain (see the housing crisis in theU.S. – dramatic decrease of house prices = decrease of the value ofcollaterals)

S.121

2. Theory of Financial Structure2.3 Adverse Selection Problems2.3.4 Which Stylized Facts are Explained by Adverse Selection?

Excourse: Microfinance in Developing Countries

I Many small businesses with small amounts of required loans.

I Typically no collaterals!

I Consequently, extremely high interest rates for private lending or noaccess to capital.

Idea:

I Bundling several borrowers to a group (group lending). Everygroup member is liable for all repayments ⇒ screening andmonitoring task is partially shifted to the borrowers.

I Self-selection of “reliable” lenders, incentive to monitor the effortsin creating profitable business.

I Repayment scheme which incentivices monitoring. Short-runopportunistic behavior will reduce likelihood of loan prolongation orfuture loans.

However: Could lead to severe social pressure within a group.S.122


1. Credit and loans are an importnat source of financing business

I One could think that there is an incentive for a firm to financetheir business primarly by selling equities (e.g. stocks), sincethe stock owner only have claims on the residual profit.

I Due to information asymmetries about risky business projectsthe owner of financial funds prefer to buy assets with a lowerrisk like bonds, or to buy “risk-free” assets like time depositswhich are used by the financial intermediates to providecredits.

I Financial intermediates have lower costs to achieveinformation about the risky business.

S.123


Source: Allen & Overy, Corporate Funding Monitor 2016 (www.allenovery.com)

(See this source also for region-specific funding structure.)

S.124


2. Indirect Financing via Intermediates (like banks) is much moreimportant than Direct Financing

I The same argument applies

3. The financial system is one of the most regulated sectors in theeconomy.

I Regulation is needed to alleviate the problems of informationasymmetries.

S.125


4. Large well-established firms have a more easy access to financialfunds than small or new firms.

I Large firms have more expertise as well as more economies ofscale to provide detailed information.

I Only large firms are rated by rating agencies.

I Well-established firms have built up reputation.

I Large firms can provide much more collaterals.

5. Collaterals are a prevalent ingredient of loan contracts for firmsand households.

I Collaterals lead to a drastic decrease of risk premiums whatalleviates the adverse selection effect.

I Combining different interest rates and collateral requirementsmay lead to self-selection (separating eqilibrium).

S.126

2. Theory of Financial Structure2.4 Moral Hazard Problems

Outline:

2.4.1 Introduction into Principal-Agent-Problems

2.4.2 How Moral Hazard Affects the Choice Between Debt andEquity

2.4.3 Solving Moral Hazard Problems

2.4.4 What Stylized Facts are Explained by Moral Hazard?

Literature:


Wolfstetter, E. (1999), Topics in Microeconomics. Cambridge University

Press, chapter 11

S.127

2. Theory of Financial Structure2.4 Moral Hazard Problems2.4.1 Introduction into Principal-Agent-Problems

General Structure:

I Principal offers a contract to the agent.

I The payoffs depend on the unobservable behavior of the agentas well as on stochastic variables.

ExamplesI Employer-employee relationship: The outcome for the employer

depends on the unobservable effort of the employee.I Borrower-lender relationship: The risk of debt failure depends

on the project choice of the borrower (high risk or low risk)

I The agent has an incentive to exploit the unobservability ofhis choice in order to maximize his own utility instead ofmaking decisions in accordance to the preferences of theprincipal (= moral hazard). This can be anticipated by thepricinpal.

S.128


Fixed payments for A, residual payments for P:

P A

equity contract

reject

(reservation utilities)

accept

A

(uP(eL, s), uA(eL, .))

(uP(eH , s), uA(eH , .))

low effort eL

high effort eH

(effort cannot be observed by P

because of stochastic variable s)

S.129


Fixed payments for P, residual payments for A:

P A

debt contract

reject

(reservation utilities)

accept

A

(uP(rL, s), uA(rL, .))

(uP(rH , s), uA(rH , .))

low risk project rL

high risk project rH

(choice of risk cannot be observed by P

because of stochastic variable s)

S.130


Resut from previous graphics:

I The principal is able to observe the outcome of the agent’sdeicion, not the decision itself = hidden action.

I This could be avoided by monitoring but we assume thatmonitoring is not possible or too expensive.

I Therefore, the contractual payments can depend on theoutcome but not on the behavior of the agent.

I The task is to design the incentive structure of the contractsuch that the Moral Hazard problem is mitigated.

S.131


Two applications:

I Agent = manager: In case of equity contracts the agent tendsto reduce his effort, since the equity holder benefits from thereturns due to his efforts. In case of a debt contract, thelender receives fixed payments, and the agent has an incentivefor high efforts since he benefits from the increasing expectedreturn.

I Agent = investor: In case of debt contracts the agent tends toinvest into too risky projects than negotiated with thelender. The reason is that in case of negative returns of theproject the debt fails = the lender also carries the risk. Therisk of the agent, however, is limited.

⇒ How to construct a financial contract which incentivices theagent to decide according to the principal’s preferences?

S.132

2. Theory of Financial Structure2.4 Moral Hazard Problems2.4.2 How Moral Hazard Affects the Choice Between Debt and Equity

Contracting with Moral Hazard:

I The financial contract regulates how the (stochastic) returnand how the risk is allocated to the principal and the agent(risk-return-scheme).

I Each type of a risk-return-scheme incentivices a certainbehavior of the agent.

I The principal anticipates the incentive structure of the agent.He proceeds in two steps:

1. What is the optimal risk-return-scheme which incentives theagent to choose a certain project or a certain effort level?

2. Which risk-return-scheme maximizes the utility of theprincipal?

S.133


Two extreme cases:

1. Fixed payments (= low risk) for the agent,residual return (= high risk) for the principal

Examples: fixed wages in case of employer-employee-relationships; shareholder and manager of a firm with fixedsalary

2. Residual returns for the agent,fixed payments for the principal

Example: premium wages for employee and fixed return forthe employer; fixed interest payments for the bank, residualreturn for the investor

S.134


A note on guarantees (suretyship):

I Guarantees from third parties (like government) reduces therisk of the lender in case of a credit failure.

I The lender has a bias towards financing too risky projects.

I Similar to Moral Hazard effects in case of insurances.

I Example: bank crisis in 2008 – if large banks could expectthat in case of insolvency there will be a governmental bailoutthey might be less cautious in buying risky assets.

S.135

2. Theory of Financial Structure2.4 Moral Hazard Problems2.4.3 Solving Moral Hazard Problems

Equity markets:

a) Monitoring:

I Providing information about the decisions of the agent andtheir consequences for earnings and profits. Thus, the actionsare less “hidden”.

I This is costly!

I Legal constraints.

I If there are many principals, a free-riding problem arises.

S.136


b) Governmental Regulation:

Same argument as in case of adverse selection (see above).

c) Co-determination of management decisions

This is possible in case of financial intermediation: Financial fundsare given to a FI (e.g. an investment corporation) that buysequities of a firm but also participate in the management.

S.137


d) Manager contracts

If managers are payed according to the impact of their decisions onthe firm value (e.g. by stock options), it could be expected thatthey have similar preferences than other holders of equity shares.

e) Mixing with debt contracts

Similar effect: The lender receives fixed payments, the agentreceives the residual profit. He will show more effort and chooseprojects according to his risk preferences.

S.138


Especially in loan markets:

a) Net Worth

Sum of assets minus liabilities = Net Worth. A failure of theproject (negative returns) reduces the agent’s own net worth.Hence agent has incentive to choose projects with proper riskinstead of exploiting the moral hazard effect and shifting the risk ofloss to the lender.

b) Collaterals

Most debt contracts contain covenants to keep some valuablecollaterals. In case of debt failure the lender can claim thesecollaterals. This works similar to the net worth effect (see above).

S.139


c) Provision of information / Monitoring

The debt contract contains covenants that the borrower mustprovide (regularly) information about his activities. There may becontractual penalties in case of verified false information.

d) Financial intermediation

Restrictions in contracts must be monitored and enforced.Intermediates can do this more effectively and at lower transactioncost than an individual lender.

S.140


Summary:

I Moral Hazard (MH) arises in both, equity and debt contracts.

I MH may result in (a) too low effort of the agent, (b) choosingtoo risky projects.

I Financial contracts should be designed in an incentivecompatible way, i.e. that agent’s utility maximizing decisionsare compatible with the preferences of the principal. This isnot always perfectly possible.

I Financial intermediates have better possibilities to alleviatethe MH problem.

S.141

2. Theory of Financial Structure2.4 Moral Hazard Problems2.4.4 Which Stylized Facts are Explained by Moral Hazard?

1. Credit and loans are an importnat source of financing business

2. Indirect Financing via Intermediates (like banks) is much moreimportant than Direct Financing

3. The financial system is one of the most regulated sectors in theeconomy.

5. Collaterals are a prevalent ingredient of loan contracts for firmsand households.

6. Debt contracts are typically complicated and contain manyrestrictions on the behavior of the borrower.

S.142

2. Theory of Financial Structure2.5 Efficient Market Hypothesis and its Limits

We leave the theory of financial intermediation and turn tosecondary markets where financial assets are valued by marketparticipants.

I Mishkin, Frederic S. (2012), The Economics of Money,Banking, and Financial Markets, 10th ed., Boston et al:(chapter 7)

I Malkiel, B.G. (2003), The Efficient Market Hypothesis and ItsCritics. Journal of Economic Perspectives 17(1), 59-82

S.143


I Study of behavior of stock prices by L. Bachelier (1900):random character of stock prices.

I E. Fama (1960ies):I Started as a “technical analyst”: trying to find “patterns” in

past data which enables investor to predict stock pricesI But: Random Walk – successive price changes are

independent⇒ interpreted RW as an indicator that all relevant information is

processed efficiently!

S.144


Idea:

I If we could predict in t from available information that pricept+1 will exceed pt then it would be rational for allparticipants to buy in t (speculation). Thus, pt willinstantanously increase until the level pt+1 so that pt is thebest predictor for pt+1.

I Thus speculation is seen as an activity making marketsinformationally efficient.

S.145


“An efficient market is defined as a market where there are a largenumber of rational profit-maximizers actively competing, with eachtrying to predict future market values of individual securities, andwhere important current information is almost freely available toall participants [...] on average, competition will cause the fulleffects of new information on intrinsic value to be reflectedinstantanously in actual prices. ” (Fama 1965)

I “Informational no-arbitrage”: a further analysis is useless

I Not possible to “beat the market” (generate excess returns)

I Consistent with the “Rational Expectations” Hypothesis

S.146


Lot of empirical work in late 1980ies. Resume in Fama (1970,Journal of Finance), elaborated EMH in three forms:

I Weak efficiency: prices fully reflect all information from pastdata (technical analysis cannot have any advantages); nosystematic market inefficiencies which could be exploited.

I Prices should follow Random Walk ⇒ testable hypothesis

I Mixed evidence: main problem is the “momentum effect”(persistence of temporary trends); episodes of euphoria andglooms.

I Example: Pesaran, M.H. (2010), Predictability of AssetReturns and the Efficient Market Hypothesis. CESifo WorkingPaper No. 3116.

S.147


I Semi-strong efficiency: prices fully reflect all informationfrom past data and all current information which is publiclyavailable.

I New informations which are relevant for fundamental value ofthe asset are incorporated in the prices immediately.

I Returns from an asset: general market moves versus individual(residual) component. Which informations drive the residualcomponent? E.g.: announced stock splits, quarterly earningsreports, issuing new stock shares, other relevant information

I Mainly empirical support of semi-strong efficiency, but resultsdepend on methodology. i.e. identification of informationalshocks.

S.148


I Strong efficiency: same as semi-strong but also incorporatingprivate information of market participants.

I However: in most legislations this is forbidden (insider trade).

I Not much evidence for strong efficiency.

S.149


Implications of EMH:

I Only surprising news are moving the market (very quickly).Published information which has been anticipated already,does not move the prices.

I Don’t trust “hot tips” (either forbidden insider trades, oruseless)

S.150


Critique:

I Micro-perspective:

I Bounded rationality, various cognitive biases (“anomalies”)which prevent even sophisticated people to make statisticallycorrect predictions (e.g. over-confidence, distortedrisk-perception)

I Herding behavior, irrational exuberance.⇒ Behavioral Finance

I Macro-perspective:

I Bubbles and crashes; global financial crisis

(Note: Eugene Fama and Robert Shiller as well as Lars Peter Hansen won 2013

the Nobel Memorial Prize in Economics....)

S.151


However:

I Fama argues that “bubbles do not exist”: a theory whichdefines and explains bubbles should be able to predict them.As long as there is no such a theory there is no reason to“believe” in bubbles. They are seen as an ex post attributionof an observed rapid price decline.

I Detection of a “bubble” requires that we know somethingabout the “fundamental value”. According to EMH, allrelevant information about this is already included in the price.Thus a sudden crash could be explained by the occurence ofnew (even small) information triggering the expectations.

I Problem of self-reference of rational expectations:expectations about future fundamental firm value⇒ Fundamental firm value: NPV of future expected cash flow.

S.152


Methodological Problem:

I To test efficiency, the modeler has to consider all relevantinformation which is necessary to compute the “best”prediction.

I If test does not reject EMH, we cannot reject that marketparticipants are doing the same as the modeler.

I If test rejects EMH: “shows that the underlying model is notcompletely specified” (e.g. the modeler did not use all theinformation which the market participants have used).

⇒ Then, EMH is not really testable ⇒ ???

I If information processing is costly but all relevant informationsare already reflected in the prices, who has an incentive tocollect and process informations? ⇒ paradox

S.153

3. The Money Supply Process3.1 Function and Measurement of Money

Outline:

3.1.1 Functions

3.1.2 Monetary Aggregates

3.1.3 Other Definitions of Money

Literature:

Bofinger (2001), chapter 1


S.154

3. The Money Supply Process3.1 Function and Measurement of Money3.1.1 Functions

”Money is what money does. Money is defined by its

function.“ (J. Hicks 1976)

Functions:

I Medium of Exchange

I Unit of Account

I Store of Value

S.155


Medium of Exchange:

I Without money each good can possibly exchanged with eachother good (bartering). Hence we have for n goods n(n− 1)/2exchange relations = relative prices.

I Finding a transaction partner with symmertic exchange wishes(A: books → whiskey, B: whiskey → books) is extremelyexpensive ⇒ transaction costs. Since there are numerouspossibilities to exchange goods “over several edges” (e.g.books → butter → cutting hair → whiskey) there are extremehigh information costs to find the best exchange relation.

I Money as a generally accepted medium of exchange leads to adramatic decrease in transaction costs (only n money prices).

S.156


Unit of Account:

I Money as a numeraire: Money prices makes comparisons veryeasy (what is “cheap”, what is “expensive”?), hence moneyreduces information costs.

I Money as a precondition for accounting systems: A generalunit enables accounting systems like balance sheets to measurethe financial wealth or current accounting systems to measurethe inflow and outflow of money and eranings per period.

S.157


Store of Value:

I Receiving money (instead of goods or services) enables themoney holder to buy goods and services to an arbitrary time.His purchaising power is conserved.

I If the disposition of the agent changes over time, the storedmoney can be used for varying expenditures → concept ofliquidity, money as the asset with the highest degree ofliquidity.

I The possibilities for intertemporal decisions (like savings in t0

for additional production and consumption in t1) increasedramatically with such a store of value.

I Problem: Inflation! Money may be substituted by real assets.This function of money is fulfilled by another asset.

S.158


I The functions define money in an abstract manner.

I There are different forms of apparance of money (financialassets) like currency, deposits, time deposits, checks etc.

I It is reasonable to define collections of financial assets whichare called monetary aggregates.

S.159

3. The Money Supply Process3.1 Function and Measurement of Money3.1.2 Monetary Aggregates

M1 = currency in circulation+ overnight deposits

M2 = M1 + deposits with an agreed maturity of up to two years+ deposits redeemable at notice of up to three months.

M3 = M2 + repurchase agreements+ money market fund shares+ debt securities with a maturity of up to two years

To be discussed later:

M0 = currency + reserves (required and excess reserves)(Central Bank Money, Monetary Base)

S.160


Monetary aggregates in 03/2017 (Bill. Euro)(source: ECB):

currency in circulation 1089overnight deposits 6301 ⇒ M1= 7390deposits mat. < 2 years 1307red. deposits < 3 months 2180 ⇒ M2= 10876repos 74money market fund shares 529debt sec. < 2 years 103 ⇒ M3= 11581

S.161


1980

1985

1990

1996

2001

2007

2012

0

0.5

1

·107

Year

mon

eyst

ock

M1

M2

M3

M0

(Source: ECB)

S.162


1998

2000

2003

2006

2008

2011

2014

2017

0

10

Year

mon

eygr

owth

M1

M2

M3

(Source: ECB)

S.163

3. The Money Supply Process3.1 Function and Measurement of Money3.1.3 Other Definitions of Money

Definition by the transmission mechanism

I There are different transmission theories on how monetaryshocks affects the real sphere or the inflation rate.

I Take a transmission theory: monetary aggregate M thenincludes all financial assets which are consistent with thetransmission theory.

I Advantage: If the transmission theory is “true”, the aggregateM is a good intermediate goal for monetary policy.

I Problem: If M is defined in this way then the underlyingtransmission theory can not be falsified. It is a tautology.

S.164

3. The Money Supply Process3.1 Function and Measurement of Money3.1.3 Other Definitions of Money

Econometric definition

I There are diffreent theories of money demand. In the long runit can be assumed that the money market is in equilibrium,i.e. money equals money demand.

I Take a theory of money demand. Money includes then allfinancial assets which are demanded by the agents (example:Keynes theory Ld(Y , i)). Statistical regression then decideswhether a type of financial asset is significant to explainmoney demand.

I Advantage: The definition of money is based on an economictheory rather than being arbitrary or a matter of convention.

I Problem: If M is defined in this way, the underlying moneydemand theory can not be falsified.

S.165

3. The Money Supply Process3.2 Creation of Central Bank Money (Money Base)

Outline:

3.2.1 Balance Sheets of the Financial Sector

3.2.2 Basic Operations of the Central Bank

3.2.3 Overview: Policy Instruments

Literature:

Bofinger (2001), chapter 3.1-3.3Mishkin (2010), chapter 15, parts of chapter 16ECB (2004), The Monetary Policy of the ECB (downloadable)

McLeay, M., Radia, A., Ryland, T. (2014), Money creation in the modern

economy. Bank of England, Quarterly Bulletin 2014 Q1

S.166

3. The Money Supply Process3.2 Creation of Central Bank Money (Money Base)3.2.1 Balance Sheets of the Financial Sector

central bank’s balance sheet (simplified)Assets Liabilities

• Foreign reserves F • Currency (C )

• Loans to commercial • Deposits of commercialbanks (Lc) banks (reserves) (R)

= required + excess reserves

• Securities (B)(e.g. bonds) • Net Worth

Monetary Base M0 = C + R

S.167

3. The Money Supply Process3.2 Creation of Central Bank Money (Money Base)3.2.1 Balance Sheets of the Financial Sector

commercial bank’s balance sheet (simplified)Assets Liabilities

• Reserves (R) • Loans:= required reserves – central bank loans (Lc)

+ excess reserves – inter-bank loans

• Loans (L): • Deposits of non-banks (D):– inter-bank loans – overnight deposits– commercial loans – time deposits– reals estate – saving deposits

• Bonds/Securities (B): • Other debt instruments• Currency (C)• Other assets • Bank Capital/Net Worth (BC )

S.168

3. The Money Supply Process3.2 Creation of Central Bank Money (Money Base)3.2.2 Basic Operations of the Central Bank

Central bank can create money M0:

I Non-borrowed reserves: purchasing securities (bonds) on thesecurity market: ∆B > 0

I Borrowed reserves: providing a loan to a commercial bank:∆Lc > 0

I Since there is an inter-bank market for (borrowed) reserves,the main central bank loans are also called “open marketoperations”.

I Furthermore, banks could borrow reserves overnight→ “standing facilities”.

S.169


Case 1: Central bank buys a security from a commercial bank

central bankAssets Liabilities

∆B = 100 ∆R = 100

commercial bankAssets Liabilities

∆B = −100∆R = 100

I With the additional reserves the commercial bank is able toprovide additional loans to the non-bank sector or to buyother assets. (Discussed later: banks do not lend thesereserves to the non-bank sector!)

I This is a restructuring of the bank’s balance sheet. Thebank will do this only if it is profitable.

S.170


Similar accounting records (e.g.):

I Central bank buys securities from a commercial bank and payswith currency: ∆B = ∆C .

I Central bank buys foreign reserves from a non-bank and payswith currency: ∆F = ∆C .

I etc. (see Mishkin (2010) for examples)

Reserves may be changed into currency and vice versa(no effect on M0):

∆R = −∆C

S.171


Case 2: Central bank loan to a commercial bank

central bankAssets Liabilities

∆Lc = 100 ∆R = 100

commercial bankAssets Liabilities

∆R = 100 ∆Lc = 100

I Again, with the additional reserves the commercial bank isable to provide additional loans to the non-bank sector or tobuy other assets.

I This extends the commercial bank’s balance sheet andshifts the debt/equity ratio of the liability side.

S.172


Some characteristics of the central bank loans:

I The commercial bank has to pay interest rates. These interestrates are the primary policy instrument.

I The loan contract has typically a maturity of one week orthree months (“open market operations”), or it is anovernight loan (“standing facilities”). In times of financialdistress there are also long-term contracts.

I The banks must provide securities = function of a collateral.

I When the loan is returned at the maturity date, the monetarybase M0 decreases ⇒ reverse accounting record.

S.173

3. The Money Supply Process3.2 Creation of Central Bank Money (Money Base)3.2.3 Overview: Policy Instruments

Overview over ECB policy instruments:

1. Reserve requirements: The bank must hold a part of theirdeposits as reserves. There is a need to borrow liquidity from thecentral bank.

2. Open Market Operations: The central bank provides liquidity tothe banks while the banks provide specified securities; tenderprocedures.

I Main operations: interest rates weekly adjusted; maturity 1week

I Long term-operations: interest rates monthly adjusted;maturity three months.

I Structural and fine-tuning operations: also definitve purchasesand sales of securities are possible.

3. Standing Facilities:I Short-run (overnight) loansI Overnight deposits

S.174


Reserve requirements:

I Liabilities with positive reserve ratio:

I Deposits (including overnight deposits, deposits with an agreedmaturity up to two years and deposits redeemable at a periodof notice of up to two years)

I Debt securities issued with a maturity of up to two years

I Liabilities with zero reserve ratio

I Deposits (including deposits with an agreed maturity of overtwo years and deposits redeemable at a period of notice ofover two years)

I Debt securities issued with a maturity of over two yearsI Repurchase agreements

S.175


(source: ECB)S.176


Market for (borrowed) reserves:

I Supply of liquid excess reserves e.g. in case of inflowingdeposits.

I Demand for liquid reserves e.g. in case of outflowing depositsor expansion of loans.

I Collateralized and non-collateralized borrowing.

I Interbank (money) market interest rate: e.g. EONIA (EuroOvernight Index Average)

I Since interbank loans and central bank loans are closesubstitutes, the central bank has a strong impact on themoney market rate, and it determines the circulating reserves.

I Fixed reserve supply and aggregated “net” demand forreserves.

S.177


Stylized market for reserves (graphic below):

I Net demand for reserves depends on interest rate.

I Total supply is determined by the CB (borrowed andnon-borrowed reserves).

I Standing facilities with rate i f : CB serves any demand ⇒perfectly elastic supply. Market rate cannot be higher than i f .

I Deposit facilities with rate id : below that rate demand wouldbe perfectly elastic because you could make money byborrowing from other banks and storing it at the CB⇒ cannot happen

I Assumed here: market rate i equals the policy rate im formain refinancing operations

S.178


i

reserves

demand

supply

i s

id

im = i

S.179


How CB could influence the market:

(a) M0 supply should be set such market

rate i is close to the policy rate imi

reserves

demand

supply

i s

id

im

i

S.180


How CB could influence the market: (cont.)

(b) Reducing the policy rate(s) will affect i

only with changing supplyi

reserves

demand

supply

i s0

id0

i0 = im0

i s0

= im0

id0id1

i s1

im1

i s1

i1 = im1

(c) At the ZLB the CB can achieve

negative rates by Quantitative Easingi

reservesdemandid

i0 = im0

supply

i s

i1

S.181


How to respond to a increasing demand for reserves?

(d) Full accomodation of demand shock

(stabilize i ; accomodate M)i

reserves

demand

supply

i s

id

i = im

demand

demand’

i ′

supply

(e) No accomodation of demand shock

(stabilize M; im follows market rate)i

reserves

demand

supply

i s0

id0

i0 = im0

demand

demand’

i ′i s0

i s1

id0

id0

i1 = im1

S.182


Consequence:

I CB cannot fully control both, interest rate and M0.

I They choose a point on the endogenously determined reservedemand function according to their policy goals..

I Most CB use interest rate as operational target, thus theyaccomodate demand for M0 such that market interest rateequals the target of the CB.

S.183


1999

2001

2004

2007

2009

2012

2015

0

2

4

6

Year

Main rate

Deposit rate

Standing facility

EONIA

(source: ECB)

S.184


Further (“unconventional”) monetary policy measures:

Background: monetary policy near the Zero Lower Bound (ZLB)

I Easier access to borrowed reserves: longer maturities, fullallotment, temporarily reduced collateral requirements

I Massive asset purchase programmes (“QuantitativeEasing”):

I CB buys bonds from non-bank sector via bank accounts (asthe CB can technically interact only with a bank)

I Usually high-rated governmental bonds but also other assetsmight be drawn into consideration

I This operation creates M0 as well as depositsI Problem: exit strategy? covered by the mandate of the CB?

S.185


I Enhanced communication strategies:I “Whatever it takes”I Forward Guidance: “Short-run interest rates will be low for a

long time” ⇒ according to expectations theory also thelong-term rates should decline ⇒ flatter Yield Curve

S.186

3. The Money Supply Process3.3 Multiple Deposit Creation and the Multiplier

Outline:

3.3.1 The Money Multiplier

3.3.2 Determinants of the Multiplier

3.3.3 Objections against Static Multiplier Analysis

Literature:

Bofinger (2001), chapter 3.4Mishkin (2010), chapter 16

S.187

3. The Money Supply Process3.3 Multiple Deposit Creation and the Multiplier3.3.1 The Money Multiplier

I Monetary aggregat M1 defined as

M1 = C + D (21)

with C as currency and D as deposits.

I The monetary base, “controlled” by the central bank, isdefined as

M0 = C + R (22)

where R are the reserves with

R = RR + ER = r · D + ER (23)

where RR are the required reserves and r is the requiredreserve ratio. ER are the excess reserves.

S.188


I Behavior of the non-bank public:

People have certain transaction customs. They wish to holdcurrency and deposits in a certain ratio (= assumption)

c =C

D⇒ C = cD (24)

I Behavior of commercial banks:

Due to liquidity considerations they hold excess reserves as ahigh liquidity risk-free asset (as a reaction to expected depositoutflows). The ratio of excess reserves and deposits areassumed to be

e =ER

D⇒ ER = eD (25)

S.189


Inserting (24 ) and (25) into (21) and (22) we have:

M0 = cD + rD + eD = (c + r + e)D (26)

M1 = cD + D = (1 + c)D (27)

Solving (26) to D and inserting into (27) we have the moneymultiplier

M1 =1 + c

r + c + eM0

∆M1

∆M0=

1 + c

r + c + e≡ m (28)

From (26), the deposit multiplier is

∆D

∆M0=

1

c + r + e(29)

S.190

3. The Money Supply Process3.3 Multiple Deposit Creation and the Multiplier3.3.2 Determinants of the Multiplier

I Required reserve rate r : fixed by the central bank; negativecorrelation with the money supply.

I Currency/deposit ratio c : depends on the behavior ofnon-banks; negative correlation with the money supply (thechange of the denominator is relatively large compared to thechange of the numerator).

I Excess reserves/deposit ratio e: depends on bank behavior ;negative correlation with the money supply.

⇒ What drives c and e?

S.191


I Excess Reserves are an asset with low return, no risk, and highliquidity. Bank holds excess reserves e.g. to meet depositoutflows or, generally, to avoid illiquidity.

I If the interest rate (for bonds and/or loans) increases, theopportunity costs of holding excess reserves increase. Hence,the excess reserves are negatively correlated with i .

I Excess reserves can be lend to other banks (inter-bankmarket). This depends primarily on trust, and also on thedifference between money market rate and central bank’sdeposit rate.

I Normally, excess reserves do not play a major role, the effctson the multiplier are small.Exception: Financial crisis 2008/2009 – sharp increase of E !

S.192


Excess reserves:2

00

0

20

02

20

05

20

08

20

10

20

13

20

16

0

0.5

1

·106

Year

exce

ssre

serv

es

(Source: ECB)

S.193


(Source: Mishkin (2006), p.381)

S.194


I For the determination of c we have no theory about paymentcustoms.

Further determinants of M1 = m ·M0:

I The money base M0 changes according toI the central bank’s activities on the security market

(purtchasing/selling bonds B)I the demand for central bank loans Lc

I The major policy instrument is Lc . Central bank can reducedeposit rate but cannot force banks to demand Lc . They canalso not completely refuse to provide Lc in case of strongliquidity needs ⇒ market interest rate would increase, losingcontrol over the interest rate.

S.195

3. The Money Supply Process3.3 Multiple Deposit Creation and the Multiplier3.3.3 Objections against Static Multiplier Analysis

The static multiplier approach M1 = m ·M0 suggests that thecentral bank is able to determine money supply. However, there aresome objections:

I The approach suggests that the multiplier process is initiated by thecentral bank, not by the demand for loans (deposits). However,credit demand initiates the demand for M0 which is thenaccomodated by the CB.

I It is assumed that additional reserves are transformed intoadditional credits. But credit supply and demand behavior is notfounded by microeconomic reasoning. Thus, you cannot “push” Mby an increase of M0.

I The determinants c , e are assumed to be fixed in the multiplierprocess. But the behavior of banks and non-banks may changebecause the multiplier process takes place since it affects e.g.interest rates and liquidity positions. Furthermore, if a monetaryimpulse has real effects (e.g. Y increases) then this has a feedbackon credit demand.

S.196

3. The Money Supply Process3.3 Multiple Deposit Creation and the Multiplier3.3.3 Objections against Static Multiplier Analysis

20

00

20

02

20

05

20

08

20

10

20

13

20

16

0

5

10

Year

M3

grow

th

ref.4.5%

(Source: ECB)

S.197

3. The Money Supply Process3.4 Endogenous Money Supply

Outline:

3.4.1 Bofinger’s price theoretic model

3.4.2 The Bernanke/Blinder approach

3.4.3 Outline of an integrated model

Literature:

Bofinger (2001), chapter 3.5

Bernanke, B., Blinder, A.S. (1988), Credit, Money, And AggregateDemand. American Economic Review, Papers And Proceedings Vol.78,435-439.

S.198

3. The Money Supply Process3.4 Endogenous Money Supply3.4.1 Bofinger’s price theoretic model

Simplified version of the Bofinger model – Basic Ideas:

The multiplier approach provides no microeconomic foundationneither of the bank’s credit supply nor of the credit demand. Thisfoundation should be (partially) provided.

I The loan interest rate (“price”) coordinates supply anddemand of credits.

I In order to provide credits the bank needs reserves.

I The equilibrium interest rate on the credit market determinesthe bank’s demand on the market for (borrowed) reserves.

I The central bank can accomodate the reserve demand or itcan change the discount rate for borrowed reserves. Hence thediscount rate affects the credit supply function.

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I Simplified bank’s balance sheet: rD + L = D + Lc (a)

I Simplified central bank’s balance sheet: Lc = rD (b)

I In the simplified version there is no currency, thereforeM1 = D and M0 = R = rD and therefore m = 1/r .

I The multiplier relation is then D = mLc . (c)

The loan supply is derived from a profit maximizing calculus:

maxL

π = iL− imLc − βL2 (30)

where the term βL2 describes the increasing risk of debt failures.

In (30) we have to substitute Lc so that it depends only on L.From (a), (b), (c) it follows

L = D = mLc ⇒ Lc =1

mL (31)

S.200


I Plugging (31) into the profit function and maximization leadsto the credit supply function

L = L(i , im, β) =1

2β(i − im/m) (32)

which depends positively on i and negatively on im and β.

I On the other market side we have a credit demand functionLD(i , y) with ∂LD/∂i < 0 and ∂LD/∂y > 0.

I The equilibrium L(i∗, im, β) = LD(i∗, y) determines the

equilibrium interest rate i∗ = i∗(im, β, y).

S.201


Now we turn to the demand for reserves:

Taking the loan supply (32) and substituting L into (31) we obtainthe optimal reserve demand:

Lc(i , im, β) =1

2mβ(i − im/m) (33)

which is a linear decreasing function of im. It is parametrized bythe equilibrium interest rate on the credit market.

S.202


The Bofinger model:

im

L

iL

Lc

(a) Credit market

LS (iL, im)

LD (iL, y)

(b) Multiplier relation(c) Market for reserves

Lc (iL, im)

(d) Interest rate passthrough

i∗L (im, y)

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Interpretation:

I Upper right: The credit market with upward sloping creditsupply function (32) and a linear cerdit demand function.

I Lower right: The multiplier relation – translates the desiredlevel of loans L into the level of required reserves which areneccessary to create deposits to finance these loans.

I Lower left: The demand for borrowed reserves Lc (33).

I Upper left: The market equilibrium interest rate i∗ is animplicit function of the discount rate im. In case of linearfunctions also this relationship is linear.

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Central bank increases the discount rate im

im

L

iL

Lc

(a) Credit market

LS (iL, im0 )

LD (iL, y)


Lc (iL, im)


im0

i∗L (im, y)

im1

LS (iL, im1 )

S.205


The demand for loans increases, central bank does not adapt im (passive)

im

L

iL

Lc

(a) Credit market

LS (iL, im)

LD (iL, y0)


Lc (iL, im)


im

i∗L (im, y0)

iL

iL

yy0

LD (iL, y1)

y1

i′L

i∗L (im, y1)

Lc (i′L, im)

(e) “LM” Curve

S.206


The model has implications for the macroeconomic IS-LM analysis:

I Demand shocks on the credit market may lead to a reactionof the central bank. Depending on their primary goals(stabilizing the interest rate vs. stabilizing the money base)different types of LM curves occur.

I If the central bank does not respond to the demand shock, anincreasing y leads to an increasing credit demand and thus toa monetary expansion. In the traditional IS-LM analysis this isnot the case.

⇒ Money creation is (partially) demand driven.

S.207


Increasing income Y1 → Y2 leads to a right-shift of money demand(credit demand) and hence to a shift of the demand for borrowedreserves.

I Case 1 – Money volume targeting: Central bank will keepthe money quantity on the same level. It has to increase thediscount rate. This leads to a left-shift of the credit supplycurve. The LM curve will be steep.

I Case 2 – Discount rate targeting: Central bank will keepthe discount rate on the same level. Hence it will provide morecentral bank loans and the money volume increases. The LMcurve will be more flat (positively sloped ⇒ previous graphic).

I Case 3 – Loans rate targeting: Central bank will keep theinterest rate on the loans market on the same level. It willfully accomodate the additional money demand by decreasingthe discount rate. The LM curve will be horizontal.

S.208


Case 1:

im

L

iL

Lc

(a) Credit market

LS (iL, im0 )

LD (iL, y0)


Lc (iL, im)


im0

i∗L (im, y0)

iL

iL

yy0

LD (iL, y1)

y1

LS (iL, im1 )

i∗L (im, y1)

Lc (i′L, im)

im1

i′Li′L

(e) “LM” Curve

S.209


Case 3:

im

L

iL

Lc

(a) Credit market

LS (iL, im0 )

LD (iL, y0)


Lc (iL, im)


im0

i∗L (im, y0)

iL

iL

yy0

LD (iL, y1)

y1

i∗L (im, y1)

im1

LS (iL, im1 )

(e) “LM” Curve

S.210


Summary:

LM curvesiL

y

i0

y0

(stabilizing M)

(passive accomodation)

(stabilizing iL)

S.211


I Don’t confuse these “LM curves” with the LM curve of thestandard Keynesian IS-LM model. The latter assume a fixedM, determined by the central bank. This is only a very specialcase in the Bofinger framework.

I For most “LM curves” in this framework there is no fixed (butan endogenously determined) money supply.

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3. The Money Supply Process3.4 Endogenous Money Supply3.4.2 The Bernanke/Blinder approach

Assume that the commercial bank’s balance sheet is

rD + E︸︷︷︸R

+L + B = D

→ E + L + B = (1− r)D

where B are bonds. The is no currency C and no central bankloans Lc . The central bank determines the money base R bypurchasing or selling bonds.

Note that M0 = R and M1 = D.

The activity of the bank is to choose an appropriate portfoliostructure of the asset side.

S.213


The asset side contains two risky assets L and B, and a risk-freeasset E . The structure of the portfolio is given by:

E (i) = λE (i)(1− r)D

L(i , ρ) = λL(i , ρ)(1− r)D

Bb(i , ρ) = (1− λE (i)− λL(i , ρ))︸︷︷︸λB(i ,ρ)

(1− r)D

where i is the interest rate of the bonds, ane ρ is the interest rateof loans.

The portfolio share λL ∈ [0, 1] depends positively on ρ, negativelyon i , and vice versa for λB , λE depends negatively on i .

S.214


The reserves of the commercial bank are

R = rD + E = rD + λE (i)(1− r)D = (r + λE (i)(1− r))D (34)

Hence the money multiplier is

∆D

∆R= m(i) =

1

r + λE (i)(1− r)

The multiplier depends on the bank’s portfolio considerations andis endogenously determined by the bonds interest rate i . Note,that i is determined on the bonds market and that the centralbank is an agent on the bonds market.

S.215


The equilibrium on the credit market is determined by

Ld(i , ρ, y) = L = λL(ρ, i)(1− r)D

It is assumed that loan demand is determined by i (+) and ρ (-)and y (+).

Money supply is given by the multiplier D = m(i)R while themoney demand follows the standard assumptions Dd(i , y)(positive dependency on y and negative dependency on i).

Money market equilibrium is given by (LM curve)

Dd(i , y) = m(i)R

S.216


Comparison:

Bofinger model:

I only borrowed reserves = discount rate policy

I banks have only loans as an asset, no portfolio approach

I Fixed multiplier, but an endogenously determined money base

Bernanke/Blinder model:

I only non-borrowed reserves = open market operations on thesecurity market

I banks use a portfolio approch to determine their portfolio whichcontains loans, bonds, and excess reserves

I Exogenously determined money base, but an endogenouslydetermined money multiplier

S.217

3. The Money Supply Process3.4 Endogenous Money Supply3.4.3 Outline of an integrated model

Remind the stylized balance sheet of a bank:

Assets LiabilitiesI Reserves (required, excess)

I Cash

I Securities/Bonds

I Loans to non-banks

I Inter-bank loans

I Deposits

I Inter-bank loans

I Central bank loans

I Other debt instruments

I Bank Capital / Net Worth

S.218


I Bank decides aboutI structure of the asset sideI structure of the liability sideI size of the balance sheet

I Decisions depend on expected returns, risks, and liquidity ofassets, as well as the interest rates to be paid for deposits,interbank and central bank loans (costs).

I Decisions are made under constraints such like Basel II/III.

S.219


I Bank create deposits by issuing loans (and also by purchasingbonds).

I Hence, the loans and bonds supply and demand determine thedeposit volume. This creates demand for reserves.

I Central bank influences (not: determines) this process by theconditions for borrowing reserves, amount of non-borrowedreserves, the required reserve rate: The elasticity how loansupply depends on these monetary policy variables, but alsoon other endogenous variables.

I Central bank has to respond to changes e.g. on the loansmarket and to changed reserve demand. Central bank’s role ina phase of financial distress.

I Increased role of non-bank financial intermediates (“shadowbanks”) – might change the transmission of monetary policyand even the ability of the central bank to affect the liquidity.

S.220

3. The Money Supply Process3.4 Endogenous Money Supply

Some Implications:

I Monetary policy has some impact on the money supply butdoes not control it. Monetary expansion is primarlydetermined by the money demand of the non-bank sector.

⇒ If money is created according to the money demand, it isquestionable to construct a “money market equilibrium”(supply = demand) like the conventional LM curve.

I Inflation by monetary expansion is therefore not only a matterof a “wrong” central bank policy but a consequence ofmassive credit expansion e.g. by governmental debt. Successof monetary policy depends also e.g. on fiscal discipline.

S.221

4. Theory of Money Demand4.1 Keynesian Theory of Liquidity Preference

Outline:

4.1.1 Transaction Motive

4.1.2 Money as an asset

4.1.3 Precautionary Motive

4.1.4 Evidence

Literature:



S.222

4. Theory of Money Demand4.1 Keynesian Theory of Liquidity Preference4.1.1 Transaction Motive

I Money is used for transaction purposes:

Mv =∑i

piqi

with M = money (stock variable), v = velocity, pi , qi as theprices and the quantities determining transaction i in theperiod (flow variable).

I Since there is no statistical data about all transactions, we usethe price index P and the real income Y as a proxy:

Mv = PY ⇒ M

Pv = Y ⇒ M rv = Y (35)

I The velocity v is a matter e.g. of payment customs.Eq. (35) is called the quantity theory of money.

S.223


(Source: ECB (2001))

S.224


Own calculations based on nominal GDP EU28 / M3 (yearly average of

monthly M3 data)

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

2011

2012

2013

2014

2015

2016

1.4

1.6

1.8

2

Year

velo

city

S.225


I If money is primarly needed for planned transactions, thedemand for money is (so called Cambridge form)

Md =1

vPY = kPY

or in real terms

Md

P≡ LT (Y ) = kY (36)

I This is the only motive in “classical” (pre-Keynes) economics.

I While the quantity theory (35) is a pure definition (and hencealways “true”), the Cambridge form (36) is interpreted as abehavioral hypothesis.

S.226

4. Theory of Money Demand4.1 Keynesian Theory of Liquidity Preference4.1.2 Money as an asset

I Keynes assumes that agents could choose to hold eithermoney or bonds as a financial asset.

I Money: No return, no riskI Bonds. Positive return, positive risk

I Assume that bonds have no maturity date and are held foronly one period (no discounting).

I Agents are assumed to be risk-neutral = they decide onlyaccording to expected return.

S.227


Bt price of the bond in tBet+1 expected price in t + 1

C regular coupon rate payments

The effective interest rate is defined by

it =C

Bt⇒ Bt =

C

itHolding the bond for one period is profitable if

π = C + Bet+1 − Bt > 0

⇒ C +C

iet+1

− C

it> 0

⇒ 1 +1

iet+1

− 1

it> 0

⇒ it >iet+1

1 + iet+1

= ic

S.228


I For it > ic there are positive returns from holding the bond,and negative returns in case of it < ic .

I Depending on individual expectations iet+1 the agent will holdfinancial wealth either in bonds or in money.

I Similar calculations can be made for the case that money (e.g.deposits) have a positive interest rate.

I Different individuals have different expectations iet+1 andhence different ic . If market interest rate falls, more and moreindividual critical interest rates are undercut, and more andmore individuals sell bonds and hold money instead.

S.229


Money demand – speculation motive

(a) individual demandiL

LS

ic

(a) aggregated demandiL

LS

ic1

LS1

ic2

LS1+LS2

ic3

LS1+LS2+LS3

S.230


The money demand from the asset motive(or as Keynes said: “speculation”) is:

Ls = Ls(i),dLSdi

< 0

Note:

I The money asset LS is limited by the financial wealth: LS incase of money is the unique asset type for all individuals.

I If you consider other alternatives than “bonds” (e.g. timedeposits), there is a dependency on multiple interest rates.

I Instead of interest rate it may be plausible to use real interestrates since LT , LS are real values.

S.231


I Bringing both motives together, we have the money demand

L = L(Y , i), with∂L

∂Y> 0,

∂L

∂i< 0

I Defining the velocity by

v =Y

M r=

Y

L(Y , i)

Keynes’ liquidity preference theory can be interpreted as theCambridge approach with an endogenous velocity:

L =1

v(Y , i)Y = k(Y , i)Y

S.232

4. Theory of Money Demand4.1 Keynesian Theory of Liquidity Preference4.1.3 Precautionary Motive

I Money is hold to make unexpected transactions = to avoidilliquidity in case of necessary unexpected transactions.

I Money holder faces opportunity costs i .

I Also from this motive we have a dependency fromY (+) and i (-):

LP = LP(Y , i)

I Original Keynesian idea: liquidity preference (hording) as aresponse to fundamental uncertainty because liquidity can betransformed in everything if the economy evolves in anunperceived way, and if people lack knowledge to form reliableexpecattions about that.

S.233

4. Theory of Money Demand4.1 Keynesian Theory of Liquidity Preference4.1.4 Evidence

Empirical Evidence:

I Since the money demand reflects plans which are notobservable, it is assumed (!) that the money market is alwayssufficiently close to the equilibrium, i.e. that real moneycirculation is a good proxy for the money demand.

I For M r = L(Y , i) we assume a log-linear form like

lnM rt = β0 + β1 lnYt + β2it + εt

where β0, β1, β2 are coefficients to be estimated, and εt is aserially uncorrelated stochastic variable.

I Derivation with respect to time t shows that

β1 =d lnM r/dt

d lnY /dt≈ dM r

dY

Y

M r

is the income elasticity of money demand, while β2 is thesemi-interest rate elasticity of money demand.

S.234


Questions:

I Which monetary aggregat? (M1, M2, M3)

I Which income? → usually real GDP

I Which interest rate? → usually bond interest rates;short term, long term interest rates?

⇒ Regression analysis

S.235


Some results (details in Bofinger (2001)):

I Positive income elasticity (some studies: near 1)

I Negative interest rate elasticity (but mostly small)

I In Europe more or less stable parameters, in USA not stable(eventually due to financial innovations)

I Large monetary aggregates do not depend on short terminterest rates.

S.236

4. Theory of Money Demand4.2 Portfolio Theory of Money Demand

Outline:

4.2.1 Money and Bonds in a Portfolio Equilibrium

4.2.2 Effect of Interest Rate Changes

Literature:

Bofinger, Peter (2001), Monetary Policy: Goals, Institutions, Strategies,and Instruments. Oxford: Oxford University Press.

Thompson, N. (1993), Portfolio Theory and the Demand for Money.

Hampshire.

S.237

4. Theory of Money Demand4.2 Portfolio Theory of Money Demand4.2.1 Money and Bonds in a Portfolio Equilibrium

Keynes Speculation Motive:

I Risk Neutrality

→ only iet+1 (expected mean) is relevant

→ (0, 1)-decision between money and bonds

I Mixture of money and bonds in a population withheterogeneous expectations.

Portfolio Approach:

I Risk Aversion

→ the distribution of iet+1 is relevant

→ each individual mixes money and bonds

S.238


I Let i be the expected return from holding a bond, and σ2B is

the variance of these returns.

I Financial Wealth of an individual: FW = M + B.Let l = M/FW be the fraction of money in the portfolio,while 1− l = B/FW is the fraction of bonds.

I Expected return and risk of a portfolio unit is then

µ(l) = l · 0 + (1− l) · i (37)

σ(l) = (1− l)σB (38)

Solving (38) to 1− l and inserting into (37) gives the linearrestriction

µ = i · σσB

(39)

S.239


I We have a utility function u(µ, σ) with the standardproperties for a risk-averse agent. The indifference curve inthe (µ, σ)-space are increasing and convex (see figure).

I Maximizing utility with respect to l conditional to the linearconstraint (39) gives the tangential solution

∂u/∂µ

∂u/∂σ=

i

σB

(see figure)

I Thus, for a given (i , σB) the optimal portfolio structure isdetermined.

S.240


µ

(1− l)

σ

µ = i · σσB

(1− l) = σσB

1

u

l

S.241

4. Theory of Money Demand4.2 Portfolio Theory of Money Demand4.2.2 Effect of Interest Rate Changes

What happens if the interest rate increases from i0 to i1?

µ

(1− l)

σ

µ = i0 · σσB

(1− l) = σσB

1

l

µ = i1 · σσB

l ′

S.242


The result depends on the income and the substitution effect!Typical result: dl

di < 0 ⇒ dMdi < 0

i

M

S.243


Substitution effect:

I An increasing it makes bonds more attractive relative to money:Portfolio will be restructured in favor of bonds. This effect isunambigous (l decreases).

Income effect:

I An increasing it shifts the expected profits with given standarddeviations upwards, or shifts the risks downwards with given profits.According to the preferences, this leads to an adaption of theportfolio where the direction is ambigous: l might decrease orincrease. If it increases, it might outweight the substitution effect ornot.

I In the figure we assumed that the income effect increases l but doesnot outweight the substitution effect.

S.244


I The total effect is henceforth:

M(i) = l(i)FW ,dM

di=

dl

diFW

I Note, that money demand depends on Financial Wealth!

I Adding a transaction motive gives:

M(Y , i) = l(Y , i)FW∂l

∂Y> 0

S.245

4. Theory of Money Demand4.3 Money Demand in Intetemporal Choice of Households

A simple intertemporal household’s problem:

I Period utility from consumption: u(ct).

I Maximization of the net present value of utility

max{ct}

∞∑i=0

βiu(ct+i )

subject to a period balance constraint:

ptct + At = Yt + (1 + it−1)At−1

where At is the financial wealth (or debt) in period t.

I Problem: Where is money? How to include money in thismodel?

S.246


Suggestion 1: Cash in advance (CIA) approach

I Household has to hold money as an additional constraintbecause market transactions are facilitated by money.

I Maximization of NPV of utility subject to the period budgetconstraint and the additional constraint

Mt = ptct

Suggestion 2: Money in the Utility function (MIU) approach

I The period utility function changes to

u(ct ,Mt

pt) = u(ct ,mt)

I The period budget constraint changes to

ptct + At + Mt = Yt + (1 + it−1)At−1 + Mt−1

I Recall that money does not bear an inrterest rate, and it istreated like “another good”.

S.247


Solving the calculus (MIU approach):

max{ct}

∞∑j=0

βju(ct+j ,mt+j)

subject to

ptct + At + Mt = Yt + (1 + it−1)At−1 + Mt−1

The Lagrangian is

L =∞∑j=0

βj {u(ct+j ,mt+j)+

λt+j [pt+jct+j + At+j + Mt+j − Yt+j − (1 + it+j−1)At+j−1 −Mt+j−1]}

S.248


First order conditions (FOC) for the period t are:

∂L∂ct

= u1(ct ,mt) + λtpt = 0 (40)

∂L∂At

= λt − βλt+1(1 + it) = 0 (41)

∂L∂Mt

= u2(ct ,mt)1

pt+ λt − βλt+1 = 0 (42)

(analogously for t + 1, t + 2, ...)

S.249


From (41) we have βλt+1 = λt1

1+it. Using this for (42)

u2(ct ,mt)1

pt+ λt − λt

1

1 + it= 0

u2(ct ,mt) + ptλt − ptλt1

1 + it= 0

From (40) we have ptλt = −u1(ct ,mt). Using this we have

u2(ct ,mt)− u1(ct ,mt) + u1(ct ,mt)1

1 + it= 0

After few simple rearrangements we obtain

u2(ct ,mt)

u1(ct ,mt)=

it1 + it

Which is the money demand function!S.250


Example: u = ln ct + lnmt leads to the money demand function

mt =1 + itit

ct

so that we have again a positive dependency on consumption (orpermanent income which drives the intertemporal consumptionbehavior), and a negative dependency on the interest rate.

The interest rate represents the opportunity cost of holding money !

Note that from the household’s maximization problem we obtainalso an Euler equation for the consumption which is a dynamicequation. Therefore, the money demand (dependend onconsumption) is also dynamic in this model.

S.251

5. Central Banking and Transmission of Policy5.1 Goals of Monetary Policy

Outline:

5.1.1 Social Welfare and Inflation

5.1.2 Social Costs of Inflation

5.1.3 Operationalization of the Inflation Goal

Literature:

Mishkin (2006), chapter 18, 26


S.252

5. Central Banking and Transmission of Policy5.1 Goals of Monetary Policy5.1.1 Social Welfare and Inflation

Ultimate goal “social welfare”

I Operationalization: e.g. high employment, economic growth,price stability, balanced trade, ...

I Conflicts among the goals, e.g. price stability and lowunemployment (short-run Phillips curve)

I In many models maximizing welfare means minimizing a lossfunction, e.g. like

L = −(π − πtarget)2 − γu2, γ > 0

with u as the unemployment rate, or

L = −(π − πtarget)2 − γ(Y − Y pot︸︷︷︸y

)2

with Y pot as the potential output, and y as the “output gap”.

S.253


Reasons why most central banks are primarly focussedon the inflation goal:

I Rational Expectations and commitment problems

I Policy assignment

I Long-term orientation of the policy

S.254


Rational Expectations and Commitment problems:

I Barro, R.J., Gordon, D.B. (1983), Rules, Discretion, and Reputation in aModel of Monetary Policy. Journal of Monetary Economics 12, 101-122.

I Assume a central bank which announces the goal of zero inflation.It is always possible that the central bank is able to realize the goal.

I If the public is believing this zero inflation goal, they incorporatethese expectations in their dispositions, e.g. wage contracts.

I By doing so it is no longer optimal for the central bank to achievezero inflation. Their policy is hence time-inconsistent. It will exploitthe low inflation expectations by choosing a positive inflation rateand positive real effects on output and employment.

I Rational agents will anticipate this time-inconsistency and notbelieve the zero inflation goal.

I The only time-consistent optimal inflation rate is positive.

⇒ Rule-binding to zero inflation better than discretion.S.255


Policy Assignment:

I “Tinbergen rule” (Jan Tinbergen, 1903-1994): In a frameworkof conflicting goals you need as many instruments as you havegoals. These instruments are assigned to the goals. Nocoordination of policymakers necessary.

I Monetary Policy ⇒ assigned to the inflation goal.

I Fiscal Policy ⇒ assigned to the output goal.

I However, the requirements of the Tinbergen model (linearindependence of instruments) are practically never met! In thelatter case, a coordinated joint policy is optimal.

Tinbergen, J. (1954), Centralization and decentralization in economic policy.

Amsterdam.

S.256


Long-term orientation:

I Many macroeconomists agree (with except for e.g.Post-Keynesian macroeconomists) that in the long runinflation is a monetary phenomenon. Real economic processesdepend in the long run only on relative prices rather than onthe price level.

I Achieving a low inflation level is assumed to be good forallocation efficiency and growth.

I Hence, central bank should achieve a stable development ofmoney supply which matches with the development of the realoutput.

S.257


From the ECB’s statute (chapter II, article 2):

“To maintain price stability is the primary objective ofthe Eurosystem and of the single monetary policy forwhich it is responsible. This is laid down in the Treatyestablishing the European Community, Article 105 (1).”

“Without prejudice to the objective of price stability”,the Eurosystem will also “support the general economicpolicies in the Community with a view to contributing tothe achievement of the objectives of the Community”.These include a “high level of employment” and“sustainable and non-inflationary growth”.

S.258

5. Central Banking and Transmission of Policy5.1 Goals of Monetary Policy5.1.2 Social Costs of Inflation

1. Transaction costs for price changes (menu costs)

2. Confusion about absolute and relative price changes distortsthe allocation (loss of efficiency), i.e. there is no perfectanticipation which part of a single price change is due toinflation.

3. Distributional biases in fixed-payment-contracts: disadvantagefor the receiver as the real value of payment is reduced.

I fixed wagesI retirement pensionsI debt contracts (!)

⇒ Bias in the distribution of financial wealth, and⇒ Distortion of intertemporal allocation

S.259


Inflation and taxation

4. “Cold Progression” (nominal increase in income leads toincreasing tax rates)

5. Inflation reduces real net interest ratesI Fisher equation: i = r + π (with πe = π)I After taxation with tax rate t:

rN = (r + π)(1− t)− π

rN > 0 ⇐⇒ r >tπ

1− t

Inflation reduces the incentive to invest.

π

t (tax rate)1

r3r2r1

S.260


6. Money loses its function as a “store of value”: Inflation raisesthe opportunity costs of holding money (like a “tax” onholding money).

⇒ Sub-optimal level of holding money. Other assets serve as asubstitue for storing purchasing power, e.g.foreign currency (⇒ depreciation of domestic currency),real estate or gold (⇒ with accompanying price effects)

⇒ This distorts the portfolio structure.

Some negative aspects occur only in case of unanticipatedinflation. However, the higher the inflation rate, the higher is thevolatility.

S.261

5. Central Banking and Transmission of Policy5.1 Goals of Monetary Policy5.1.3 Operationalization of the Inflation Goal

Price index:

I Two common concepts:Laspeyres-Index PL and Paasche-Index PP

PL =

∑ni=1 p

ti q

0i∑n

i=1 p0i q

0i

, PP =

∑ni=1 p

ti q

ti∑n

i=1 p0i q

ti

where pji is the price of good i in period j (with j = 0 as the

base period) and qji as the quantity share in the basket.

I The shares qji may be adjusted according to the “consumerbehavior of a typical houshold”.

I Different price indices e.g. for consumer prices. In Europe:HCPI according to the Laspeyers concept.

I GDP-deflator according to the Paasche concept.

S.262


Inflation target of the ECB:

“... narrow below 2% of an increase of the HCPI.”

Why not zero inflation?

I The HCPI (as all Laspeyres indices) overestimates inflation.

I Recall thatr = i − πe

If πe = πtarget = 0 in case of a credible announcement, it ismore likely that i approaches the Zero Lower Bound. Withπtarget > 0, instead, it is still possible to stimulate theeconomy in case of a negative shock by setting i close to zero(negative r).

I Since πtarget could not exactly be achieved (stochastic effects)and deflation causes more welfare losses than inflation, asmall positive rate minimizes the expected losses.

S.263


deflation inflation π

loassesE [losses]

S.264


Biases in the inflation index:

I Quality bias (example: computer)

I New goods bias (example: consumer electronics)

I Relative price changes lead to substitution effects which arenot incorporated in the fixed q0

i .

I There is not a single price for a good but a price dispersion;while pji reflects an average price, consumer tend to chooselow price offers.

S.265

5. Central Banking and Transmission of Policy5.2 Transmission Mechanisms (Channels)

Outline:

5.2.1 Preliminaries

5.2.2 Quantity Theory as a Black-Box Approach

5.2.3 Money View: Focusing the Interest Rate

5.2.4 Credit View: Focusing the Lending Activities

5.2.5 Expectation Channels

Literature:



S.266

5. Central Banking and Transmission of Policy5.2 Transmission Mechanisms (Channels)5.2.1 Preliminaries

I There exist different causal relationships between policyinstruments, intermediate targets and final goals.

I The magnitude of effects depend on the value of exogenousand endogenous variables.

I The effects occur with time lags (timing of monetary policy,role of forecasts).

I The causal relationships are controversially discussed in theory(e.g. How sticky are prices? Do reserves determine lending ordoes lending determine reserves? Are investments limited bycredit rationing?).

S.267


Transmission channels might change because of (e.g.):

I new financial products and intermediaries

I increasing global integration of financial markets

I increasing global integration of goods markets

I changed behavior of banks due to regulation

I specific economic situations (e.g. ZLB)

S.268


(Mishkin (2006), p.619)

S.269


(ECB website)

S.270

5. Central Banking and Transmission of Policy5.2 Transmission Mechanisms (Channels)5.2.2 Quantity Theory as a Black-Box Approach

Causal transmission channels:

I Money View: Monetary Policy affects money market(short-term) nominal interest rates which translates intolong-term real interest rates. This has directly an effect onconsumption and investment demand via optimizationconsiderations. Interest rates also affects exchange rates (viaIRP) and the latter affects net exports demand.

I Credit View: Monetary Policy affects the conditions oflending and has therefore a quantitative effect on lendingvolume which is then financing the demand.

I Expectations: Monetary Policy communication (e.g.“Forward Guidance”) has an effect on inflation expectationsand also on the term premium (difference between short-termand long-term rates). This is more related to the “MoneyView” as this influences the long-term real interest rate.

S.271


Quantity Theory:

M · v = P · Y⇒ M + v = π + Y

⇒ m + M0 + v = π + Y

If v ≈ 0 then “too strong” money creation M > Y “leads to”inflation. Monetarism: “Inflation is always a monetaryphenomenon”.

I Forecasting: m, v , Y

I Goal: π (e.g. close to zero)

I Target: M0

Idea: M ⇒ used for transactions in goods market ⇒ Y D ⇒ P

S.272


However:

I Prices are actually made on the goods market, mainly drivenby Y d .

I The Quantity Equation is a pure algebraic relationship as thevelocity of money is defined by:

v ≡ P · YM

I Recall that M is created endogenously. Recall that creditdemand – and thus creation of deposits – might depend ongrowing demand Y D . Then inflation π is not “caused” by Mbut ı and M have both a common cause. (Empirically, the

correlation between M and Y is stronger than between M and π.)

S.273

5. Central Banking and Transmission of Policy5.2 Transmission Mechanisms (Channels)5.2.3 Money View: Focusing the interest rate

(a) The standard interest rate channel

In the IS-LM framework, central bankdetermines the money volume (shift of LMcurve). Excess supply of money leads toan excess demand of bonds. Hence thebonds price increases and the interest ratefalls: policy → M → i → I (i)→ Y D .

However, (a) CB does not “determine” M(endogeneity of M), (b) most CB consideri as the operating or intermediate targetrather than M, thus i could be seen as apolicy instrument.

i

Y

IS

LMLM’

π

Y S ,Y D

Y S

(Phillips Curve)

Y D

Y D ’

S.274


Central banks affect the short-term money market rate by both,the discount rate and also outright purchases of assetsIndependent from IS-LM, central bank affects long-term rates:

I The central bank’s discount rate but also outright purchasesaffect the money market for borrowed reserves.

I This affects the bank’s loans supply, and other dispositionsabout the bank’s balance sheet structure and size.

⇒ Effects on bonds interest rates, stock prices, and loan interestrate.

imoney → ibonds , iloans

or more generally

i safeshort → i riskylong , isafelong

S.275


Demand for investment goods:

I Investors calculate whether to invest into a physicalinvestment project I or into bonds B.

⇒ Fisher equation: real return from physical investment =nominal interest rate - expected inflation (r = i − πexp) sothat aggregated investment demand depends on real interestrate: I (r) with I ′ < 0.

I Physical investments are long-term: only long-term interestrates play a role.

I Depending on agency problems a specific finance structurewill be chosen (loans, bonds, internal finance). Bonds andloans interest rate are therefore linked to each other.

S.276


Demand for (durable) consumption goods:

I Some consumption goods (cars, furniture etc.) are financed byloans. Thus the loans interest rate affects consumtpion.

I Similar for mortgages (housing).

I In case of intertemporal optimization, also expected inflationplays a role (⇒ real interest rate)

ishort → ilong → I (rlong ),C (rlong ) → Y D

S.277


b) The Tobin-q-effect

I The market value of a firm (MVF ) reflects the discountedflow of expected returns from the asset side.

I If there is a new enterprise = a new need for productioncapacities, then it has to calculated whether(i) it is more profitable to buy an existing firm (price = MVF )

or(ii) to buy/produce new capital goods (price = costs forfinancing capital goods, CC )

S.278


I Let R be the return from the new enterprise. Then theeffective return depends on the cases (i) and (ii):

r(i) =R

MVF

r(ii) =R

CCThe demand for new investment goods requires r(ii) > r(i) or(in Tobin’s concept)

q =r(ii)r(i)

=MVF

CC> 1 (43)

I Monetary policy affects financing costs for capital as well asthe stock prices = market value of firm. An expansive policyleads to lower interest rates and higher stock prices due toportfolio rearrangements ⇒ increase of Tobin’s q ⇒stimulates investments ⇒ aggregated demand.

S.279


c) Exchange rate channel

I Interest rate parity theory (no arbitrage condition):

eexp − e

e= i − i∗

with i∗ as the foreign interest rate. With given expectedfuture exchange rate eexp and given i∗, an increase of i makesdomestic investment c.p. more attractive:

I i increases → domestic currency is appecreiated (e ↓)I i decreases → domestic currency is depreciated (e ↑)

I The exchange rate affects exports and imports and hence thetrade balance NX = Ex − Im which is a part of theaggregated income.

i → e → NX (e) → Y D

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d) Wealth effects

I Monetary policy has an effect on asset prices. An increase inasset prices leads to an increasing nominal level of financialwealth FW (and with fixed prices also real wealth).

I According to the Pigou effect a higher financial wealth FWstimulates the consumption demand (shift in theintertemporal consumption/saving decision in favor ofconsumption because FW is kept on an optimal level). Similarargument by Modigliani (1971).

i → asset prices → FW → C (FW , ·) → Y D

S.281


Remarks:

I Monetary policy does not directly determine the interest rates whichare relevant for economic decisions (long-term real rate). Varyingrisk premia and term premia have to be considered.

I How strong these effects are is an empirical question.

I Changes of the interest typically associated with changed inflationexpectations ⇒ effect on real interest rate might be different.

I Stimulating policy not possible at the Zero Lower Bound.

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5. Central Banking and Transmission of Policy5.2 Transmission Mechanisms (Channels)5.2.4 Credit View: Focusing the lending activities

Basic idea:

I Economic activities have to be financed. Due to agency problemsthe access to borrowed financial resources is contrained. Comparedto financing with retained profits there is always an externalfinance premium when borrowing these resources.

I Banks play an important role because (a) bank lending (credits) area very important financial resource as banks could (partially)manage these agency problems, (b) these bank activities areassociated with creation money (which is tied to inflation in thelong run), (c) there is direct interaction between central bank andcommercial banks.

I Empirical evidence that interest rate channel effects are relativelysmall (Bernanke/Gertler (1995), Mishkin (1005)) while constraintsdue to agency problems seem to be important (Gertler/Gilchrist(1993)).

I Credit view looks to the balance sheets of both, lender and borrower.S.283


a) Bank lending channel

I Looking to the balance sheet of the lender (bank).

I Loans supply is tied to monetary policy via the availability ofreserves. Thus the amount of non-borrowed reserves as well asthe discount rate for borrowed reserves affect the costs ofproducing a loan (loans supply function).

I Untightening monetary policy improves supply side:I Lower refinancing cost ⇒ right-shift of loans supply functionI Induced lower interest rate reduces adverse selection problem

and could reduce external finance premium (reduction of riskpremium).

reserves → availability of loans and deposits → I ,C → Y d

I Although this also reduces the interest rate, the focus is hereon the quantitative effect (additional loans which financeadditional economic activities).

S.284


b) Balance Sheet Channels

I Looking to the balance sheet of borrowers.

I Channel is based on the adverse selection and moral hazardeffects. These effects lead to credit rationing. The rationing effectcan be alleviated by collaterals and net worth, and own capital.

⇒ Monetary policy affects asset prices and thus the value of collateralsand thus net worth.

⇒ Therefore also the ratio between the value of debt and the value ofequity + net worth changes.

⇒ Lower interest rate leads to less interest rate payments = largercash flow of borrowers = lower risk of distress and default

⇒ This leads to a lower rationing effects and hence credit expansion.

→ asset prices → adverse selection/moral hazard↓ → lending → Y d

S.285


Empirical view and remarks:

I Empirically the effect of policy measures on loans have to beisolated from other supply and demand factors.

I Size and structure (e.g. liquidity, capital) of bank’s balancesheet as well as their access to external financing (other thancentral bank) seem to play a role (Kashyap et al. (1996),Kashyap/Stein (2000).

I At the ZLB there is still room for unconventional monetarypolicy measures (UMP) which affects asset prices and thebank’s balance sheet. However, the effect of UMP on banklending seem to be small.

I Are the induced changes of asset prices a problem? (Assetprice inflation, distributional effects)

S.286

5. Central Banking and Transmission of Policy5.2 Transmission Mechanisms (Channels)5.2.5 Expectation Channels

Central bank’s communication as a policy tool:

I Economic outlook and inflation forecasts ⇒ might shape the(inflation) expectations of the public.

I Credibility plus announced or observed strategies of thecentral bank shapes expectations about future monetarypolicy.

I “Forward Guidance”: e.g. promise to keep short-run interestrates low also in the future ⇒ via expectations or liquiditytheory shapes the term premium and therefore the long-termrates (flatter Yield Curve).

I The “wording” of policy statements is important.

Example (FAZ 7.6.2017): Markets expect that ECB will slightlyreduce the inflation forecast. As a consequence the Eurodepreciated immediately.

S.287


I Prices and wages are more or less rigid in the short run:

I Transaction/menu costs of price changesI Negotiation costs (wage contracts) ⇒ long-term contractsI Uncertainty whether costs and/or demand has changed

systematically or due to stochastic fluctuation (informationalfrictions)

I If monetary policy affects demand, it has effects on quantitiesbut only moderate price effects in the short run.

⇒ Short run Phillips curve

S.288


What happens when these future price changes are expected?

I Economic agents will incorporate their inflation expectationsinto their contracts.

I The expectation augmented Phillips curve shifts. The realeffects of monetary policy decrease (to zero).

I Hence, monetary policy aims to keep inflation expectations ona low level.

⇒ The central bank policy has to be credible.

I Central bank not only affects inflation expecattions but alsofuture interest rate expectations (and thus long-term rates ⇒Yield Curve).

S.289

5. Central Banking and Transmission of Policy5.3 Targets, Strategies, and Rules

Outline:

5.3.1 Which targets to choose?

5.3.2 Targeting the money volume

5.3.3 Inflation Targeting

5.3.4 The Taylor Rule

Literature:

Mishkin (2006), chapter 18, 21


S.290

5. Central Banking and Transmission of Policy5.3 Targets, Strategies, and Rules5.3.1 Which targets to choose?

I Since the final goals could not be achieved directly bymonetary policy there is a need for intermediate andoperational targets.

I These targets should have the following properties:

I MeasurabilityI ControllabilityI Predictive effects on the goals (this depends on the adopted

transmission theory)I Not too long delays of the effects

I “Targets” may also be referred to as “indicators”

S.291


I Operating targets:I money market rate

I Intermediate targets:I interest ratess (loans, bonds) and their structureI money volume (M1, M2, M3)I exchange rateI output gap

I Final target:I Price level target or inflation rate target?

S.292


Intermediate targets may be conflicting!

⇒ Remind the price-theoretic model by Bofinger:

I Targeting the loans interest rate→ then the loans volume = money volume changes.

I Targeting the loans volume→ then the loans interest rate changes.

S.293


Price level target or inflation rate target?

I Price level target: p∗t (example: p∗t = p∗)

I Inflation rate target: π∗ (example: π∗ = 0)

I Both targets are equivalent in case of perfect control!

I Differences occur in case of imperfect control (control errors)

S.294


Evolution of the price level with a fixed inflation rate p∗ incontinous time:

pt = eπ∗tp0 ⇒ ln pt = ln p0 + π∗t

ln pt+1 = ln p0 + π∗(t + 1)

= ln pt + π∗

if there are no control errors. Including control errors we have

ln pt+1 = ln pt + π∗ + ζt

with E [ζt ] = 0,Var [ζt ] > 0and it is serially uncorrelated. How to respond to these errors?

S.295


I Assume inflation rate goal π∗ = 0: Price level follows aRandom Walk, since the control error is neutral there is noneed to adapt policy measures:

ln pt+1 = ln pt + ζt

I Price level goal p∗: Random deviations from the price levellead to adaptions of the policy measures:

ln pt+1 = ln pt + λ(ln p∗ − ln pt) + ζt , λ ∈ (0, 1)

Result of control errors:

I Price level is more volatile in case of inflation goal.

I Inflation rate is more volatile in case of a price level goal.S.296

5. Central Banking and Transmission of Policy5.3 Targets, Strategies, and Rules5.3.2 Targeting the money volume

I The monetary policy of the Deutsche Bundesbank (beforethe monetary union) was primarly based on money volumetargets.

I Possible in a regime of flexible exchange rates (after BrettonWoods)

I Stable demand for money L(y , i), that means stablefunctional form and parameters. This has empirically provento be the case for M3.

I M1 and M2 seem to be too volatile. The Deutsche Bundebankhad chosen M0 (1974-1988), and later M3 (from 1988-2001).

I Assumption: stable relation between target M and goal π inthe long run (money neutrality).

S.297


I In accordance to quantity theory we have the“potential formula”

M3 + v trend = πgoal + Y pot

where Y pot is the (estimated) production potential. Themonetary policy has been oriented on the long run growthpath.

I The current velocity v depends on the busniness cycle(increasing in boom, decreasing in recession). An orientationon the trend of v means that the policy does not respond tobusiness cycles.

I The goal π as the “unavoidable inflation rate” is 1-2 %.

S.298


The targets for M3 is formulated

I for a certain period : e.g. 1 year

I as an average goal (the target e.g. M3 = 6% should beachieved at the end of 1 year, fluctautions within this yeardon’t matter) or as a permanent goal (the target is controlledwithin the period, e.g. every month → higher transparency ofthe policy)

I as a dot target (“exactly M3 = 6%”) or as a target corridor(“M3 = 6%± x%”). A dot target will be violated with aprobability of nearly 100%. A “broad” corridor target willrarely be violated but is not a meaningful target anymore.

S.299


Money volume targets have rarely been achieved. Nevertheless, theBundesbank policy was successful regarding the final goal ⇒importance of credible communication

(Gischer/Herz/Menkhoff (2005), p.308)S.300


The relation between money growth and inflation is

I very close if the sampleI consists of episodes with high inflationI long-run samples

(see “stylized facts” by McCandless/Weber (1995))I not very close

I in case of low inflation

Gertler, P., Hofmann, B. (2016), Monetary facts revisited. BIS WorkingPaper No. 566.

The long-run link between money growth and inflation has weakened over

time. Money-inflation nexus stronger in emerging countries but weak in

countries with low inflation and liberalized financial markets.

S.301


The long run relationship between inflation and monetaryexpansion is an argument for the “neutrality” of money.

Correlation withM0 M1 M2

all 110 countries 0.925 0.958 0.950Subsamples:21 OECD countries 0.894 0.940 0.95814 latin american countries 0.973 0.992 0.993

(Source: McCandless/Weber (1995), Some Monetary Facts, in: Federal Reserve

Bank of Minneapolis Quarterly Review, Vol.19, M.3, pp.2-11)

S.302


In the short run and/or in countries with low inflation rates thecorrelation is not very strong:

(Spahn (2006), p.116)

S.303


(Mishkin (2006), p.10)

S.304

5. Central Banking and Transmission of Policy5.3 Targets, Strategies, and Rules5.3.4 Inflation Targeting

I Rationale of Inflation Targeting: Central Bank is committedto the inflation goal for time-consistency reasons. Theyminimize

L = (πe − πtarget)2

I As a consequence (without explicitly considering amacroeconomic model) the operating target of the CB willreact to deviations from the target:

∆i = β(πe − πtarget), β > 0

I Minimization of the loss subject to macroeconomicrelationships and inflation expectations of the private sectorwill be discussed below.

S.305


Inflation targeting has been a successful policy strategy e.g. in New

Zealand, United Kingdom, Sweden, Canada.

(Mishkin (2006), p.503)

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(Mishkin (2006), p.503)

S.307


Does Inflation Targeting rule out any policy response to theoutput gap?

I Recall that monetary policy affects the real sector with lags.

I Consider the following IS curve and Phillips curve (Svensson(1997)):

πt+1 = πt + a1yt + εt+1

yt+1 = b1yt − b2(it − πt) + ηt+1

with ε, η as stochastic terms with E [εt ] = E [ηt ] = 0.

I With this structure we have it ⇒ yt+1 ⇒ πt+2.

I Hence, the goal is to achieve E [πt+2] = πtarget

S.308


Taking the Phillips curve with a further lag (t + 2):

πt+2 = πt+1 + a1yt+1 + εt+2

and using Phillips Curve for πt+1 and the IS curve for yt+1 we have

= [πt + a1yt + εt+1] + a1[b1yt − b2(it − πt) + ηt+1] + εt+2

The expected value should be equal to πtarget :

πtarget = [πt + a1yt ] + a1[b1yt − b2(it − πt)]

= [a1 + a1b1]︸︷︷︸α2

yt + [1 + a1b2]︸︷︷︸α1

πt − a1b2︸︷︷︸α3

it

⇒ it =1

α3(α1π1 + α2yt − πtarget)

which means that Strict Inflation Targeting does also consider theoutput gap yt . Literature suggests that Flexible Inflation Targeting(responding to transient stochastic output shocks) is also suitable as itdoesn’t undermine credibility of the announced inflation target.

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5. Central Banking and Transmission of Policy5.3 Targets, Strategies, and Rules5.3.5 The Taylor Rule

I Taylor, J.B. (1993), Discretion versus Policy Rules in Practice.

Carnegie Rochester Conference Series on Public Policy 9(4),

195-314I The operating target should respond to the equilibrium real

interest rate r0, the deviation of current and targeted inflationrate, as well as to the “output gap” yt = Yt − Y p

t .

it = r0 + πt + α(πt − πtarget) + βyt

(which looks very similar to the Inflation Targeting strategy.)I In case of accelerating inflation the central bank increases the

target rate (by 1 + α). In case of a boom where the outputgap becomes positive the target rate is also increased (by β).

I The response 1 + α > 1 (Taylor Principle) is importantbecause otherwise the real interest rate would decline in caseof increasing π which stimulates demand further and thusdestabilizes the economy.

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Taylor has shown that the rule is a good empirical descriptionfor the behavior of most central banks. For the USA Taylor showedthat the rule with r = 2, πtarget = 2, α = 0.5, β = 0.5 is a goodpredictor for the Fed policy.

(Mishkin (2006), p.430)

S.311


(Other empirical results)

S.312


Operationalizing the Taylor rule:

I Inflation is measured e.g. by the HCPI.

I Income is measured e.g. by the nominal GDP while theproduction potential has to be estimated (e.g. econometricestimation of a production function).

I Targets for the inflation rate and the “equilibrium” realinterest rate may be theoretically justified.

S.313


The main advantages:

I Simple and transparent heuristic rule.

I Kind of Flexible Inflation Targeting without solving anoptimization calculus (which requires full knowledge of themodel).

I Following a rule might support credibility of CB’sannouncements.

I Different macroeconomic views of the transmission process arecompatible with the rule (i.e. it does not depend critically ona specific macroeconomic paradigm).

I Empirically robust description of central bank behavior.

Problem: How to determine r0? Is it time-invariant?

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Example: Compatibility with targeting monetary aggregats

From quantity theory and the Bundesbank concept (targeting M) we have

∆M = ∆P + ∆Y −∆v

∆M target = ∆P target + ∆Y pot −∆v trend

The interest rate policy responds to the deviation from realized andtargeted values:

∆i = φ(∆M−∆M target) = φ((∆P−∆P target)+(∆Y−∆Y pot)−(∆v−∆v trend))

Explaining the short and long run change of the velocity of money:

∆v = α1∆i − α2∆Y

∆v trend = −α2∆Y pot

we obtain the Taylor rule

∆i =φ

1 + φα1(∆P −∆P target) +

φ(1 + α2)

1 + φα1(∆y −∆ypot)

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Variants of the Taylor rule:

I It is reasonable that a forward-looking central bank respondsto expected values:

i target = r + πet+1 + α(πet+1 − πtarget) + β(Y et+1 − Y pot,e

t+1 )

I Smotthing interest rates: Taylor interest rate should notfluctuate too much. Possible smoothing rule:

i smootht = λi targett + (1− λ)it−1

⇒ More information in course MW21.3 Monetary and FiscalPolicy (Prof. Wolters)

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